SEMINAR ON HARMONIC ANALYSIS AND APPLICATIONS | Year:2017 | دوره:5 |Papers Count:58

IN THIS PAPER, WE STUDY U-CROSS GRAM MATRIXES, WHICH CAN BE PRODUCED BY FRAMES AND RIESZ BASES, AND THEIR PROPERTIES. THEN WE INVESTIGATE SOME NECESSARY OR SUCIENT CONDITIONS FOR INVERTIBILITY OF THIS MATRIXES AND TRY TO RECONSTRUCT THE ELEMENTS OF L2. IT IS IMPORTANT IN APPLICATION TO STATE THE INVERSE OF U-CROSS GRAM MATRIXES AS THE FORM OF U-CROSS GRAM MATRIXES.

IN THIS PAPER BY USING THE KIRILLOV ORBIT METHOD, WE SHOW THAT THE PHASE SPACE FOR A SCALAR MASSIVE PARTICLE ON 1+1-DE SITTER SPACE IS A COTANGENT BUNDLE T* (S1) WHICH IS ISOMORPHIC TO THE COMPLEX CIRCLE S1C. THE EIGENSTATES IN ASSOCIATED HILBERT SPACE WHICH ARE THE COHERENT STATES, ARE OBTAINED FROM THE HEAT KERNEL OF COMPLEX CIRCLE. BY THESE STATES AND THE BEREZIN INTEGRAL QUANTIZATION, WE OBTAIN THE CREATION AND ANNIHILATION OPERATORS ON DE SITTER.

LET H BE A HILBERT SPACE AND B (H) DENOTES THE ALGEBRA OF ALL BOUNDED LINEAR OPERATORS ON H AND ABE A BOUNDEN OPERATOR IN H. LET A, B Î B (H) BE POSITIVE OPERATORS AND F BE A POSITIVE LINEAR FUNCTIONAL ON B (H). WE SHOW THAT, IF F IS A NON-NEGATIVE OPERATOR DECREASING FUNCTION, THEN THE FUNCTION T® F (F (A+TB)) CAN BE WRITTEN AS A LAPLACE TRANSFORM OF A POSITIVE MEASURE.

SUPPOSE A IS A BANACH COALGEBRA. A BANACH SPACE X IS CONSIDERED AS A BANACH COMODULE OVER A AND THEN AS A BANACH A*-MODULE WITH MODULE OPERATIONS J1 AND J2. WHEN X=A, IT WILL BE SHOWN THAT THE CONVOLUTION PRODUCT OF BANACH ALGEBRA A*, EQUALS TO BOTH OPERATIONS Φ*1AND Φ T*T 2. THEN SOME RELATIONS AMONG THESE OPERATIONS AND SOME DUAL OF THEM ARE INVESTIGATED.

THIS PAPER DEALS WITH THE LEGENDRE WAVELET (LW) COLLOCATION METHOD FOR THE NUMERICAL SOLUTION OF THE RADIAL SCHRODINGER EQUATION FOR FREE PARTICLE (ELECTRON) IN SPHERICAL COORDINATE. APPROXIMATELY ANALYTICAL ALSO NUMERICAL RESULTS OF THE GROUND STATE MODE L=0, OF WAVE FUNCTION OR PROBABILITY DENSITY FUNCTION R(R), HAS BEEN PRESENTED AND COMPARED WITH THE EXACT SOLUTION.

THIS PAPER IS DEVOTED TO DEFINITION STANDARD HIGHER DIMENSION SHEARLET GROUP S=R+´RN-1´ RN FOR N ³ 3 AND DETERMINATION OF SQUARE-INTEGRABLE SUB-REPRESENTATIONS OF THIS GROUP. ALSO WE IDENTIFY THE DUAL SPACE OF S.

IN THIS PAPER, WE APPLY PARSEVAL SHEARLET FRAMES TO SOLVE THE WAVE EQUATION. TO THIS END, USING THE PLANCHEREL’S THEOREM, WE CALCULATE THE SHEARLET COEFFICIENTS.

CURRENTLY, THRESHOLDING AND COMPRESSED SENSING IN COMBINATION WITH BOTH WAVELET AND SHEARLET TRANSFORMS HAVE BEEN VERY SUCCESSFUL IN INPAITING TASKS. HOWEVER, NUMERICAL RESULTS DEMONSTRATE THAT SHEARLETS OUTPERFORM WAVELETS IN THE PROBLEM OF IMAGE INPAINTING. IN THIS PAPER WE SET UP A PARTICULAR MODEL BY INSPIRED SEISMIC DATA AND A BOX MASK TO MODEL MISSING DATA. THE CHALLENGE IS TO FILL IN THE BOX THAT IS ATTENDED IN CORRUPTED IMAGES.

IN THIS PAPER WE INITIATE AND STUDY THE HECKE-ALGEBRA FOR A DISCRETE HYPERGROUP K AND ITS M-SUBHYPERGROUPH.

ONE OF THE NOTEWORTHY AMENABILITY PROBLEMS, IS TO EXPLORING ANY RELATIONSHIP BETWEEN THE AMENABILITY OF AN ALGEBRA STRUCTURE AND ITS BIDUAL SPACE. IN THIS PAPER WE CONSIDER THIS ISSUE IN THE CONTEXT OF TRIPLE SYSTEMS AND PROVE THAT A JB-TRIPLE IS TERNARYN-QUASI-WEAKLY AMENABLE WHENEVER ITS BIDUAL SPACE IS TERNARY N-WEAKLY AMENABLE.

FOR ANY LOCALLY COMPACT ABELIAN (LCA) AND SECOND COUNTABLE GROUP G, WE AIM TO CONSTRUCT A MULTIRE SOLUTION ANALYSIS (MRA) IN L2 (G) BY RIESZ FAMILY OF SHIFTS OF A REFINABLE FUNCTION J Î L 02 (G) BASED ON A UNIFORM LATTICE L IN G THAT AT FIRST, WE INVESTIGATE CERTAIN BANACH SPACES (FORMULA).

FOR ANY LOCALLY COMPACT ABELIAN (LCA) AND SECOND COUNTABLE GROUP G, WE AIM TO CONSTRUCT A MULTI RESOLUTION ANALYSIS (MRA) IN L2 (G) BY RIESZ FAMILY OF SHIFTS OF A REFINABLE FUNCTION J Î LO 2(G) BASED ON A UNIFORM LATTICE L IN G THAT AT FIRST, WE INVESTIGATE CERTAIN BANACH SPACES (FORMULA)

FIRST WE PRESENT SOME USEFUL CHARACTERIZATIONS FOR THE FUNCTION SPACES AP (G), WAP (G) AND LUC (G) ON A LOCALLY COMPACT QUANTUM GROUP G AND THEN WE STUDY SOME CONDITIONS UNDER WHICH AP (G) AND WAP (G) ARE C*-ALGEBRAS. WE ALSO INVESTIGATE THE EQUALITY LUC (G) =WAP (G).

IN THIS PAPER, WE CONSIDER THE NOTION OFK-FUSION FRAMES IN HILBERT SPACES, WHICH IS A NEW GENERALIZATION OF FUSION FRAMES. OUR MAIN PURPOSE IS TO RECONSTRUCT THE ELEMENTS FROM THE RANGE OF THE BOUNDED OPERATOR KON A HILBERT SPACE H BY USING A FAMILY OF CLOSED SUBSPACES IN H. FOR THIS END, WE INTRODUCE THE NOTION OF DUALITY FOR K-FUSION FRAMES AND CHARACTERIZE DUALS OF SOME K-FUSION FRAMES. ALSO, WE SURVEY THE ROBUSTNESS OFK-FUSION FRAMES UNDER SOME PERTURBATIONS.

IN THIS PAPER THE NEW CONCEPT OF THE QUATERNIONIC UNITARY REPRESENTATION OF A LOCALLY COMPACT GROUP TO THE UNITARY GROUP OF A QUATERNIONIC HILBERT SPACE IS STUDIED. A CONTINUOUS WAVELET TRANSFORM BY MEANS OF A SPECIAL CASE OF SUCH REPRESENTATIONS IS DEFINED TO EXTEND THE CONTINUOUS WAVELET TRANSFORM RELATED TO SEMIDIRECT PRODUCT GROUPS.

LET G BE A LOCALLY COMPACT GROUP AND P: G ® U(HP) BE A UNITARY REPRESENTATION. IN THIS ARTICLE WE WILL STUDY ON THE EXISTENCE OF AN ADMISSIBLE VECTOR FOR IRREDUCIBLE REPRESENTATIONS AND THE COMPACTNESS OF G. IN FACT, IT WILL BE SHOWN THAT IF G IS A COMPACT GROUP THEN EVERY IRREDUCIBLE REPRESENTATION OF G HAS AN ADMISSIBLE VECTOR, AND ALSO HAS A BOUNDED CYCLIC VECTOR. CONVERSELY IF G HAS PROPERTY (T) AND A FINITE IRREDUCIBLE REPRESENTATION OF G HAS AN ADMISSIBLE VECTOR, THEN G IS A COMPACT GROUP. SINCE CONTAINMENT OF AN IRREDUCIBLE REPRESENTATION L IN THE LEFT REGULAR REPRESENTATION LG IS A NECESSARY AND SUFFICIENT CONDITION FOR EXISTENCE OF ADMISSIBLE VECTOR, HENCE IT SEEMS A NATURAL OBJECT OF WEAKLY CONTAINMENT OF THESE REPRESENTATION AND THEREFORE PROPERTY (T) IS PEERED.

GIVEN A NON-ZERO NORMED VECTOR SPACE A AND A CONTRACTIVE NON-ZERO ELEMENT J Î A* (THE DUAL SPACE OF A), WE INTRODUCE THE BANACH FUNCTION ALGEBRA CJ (K), WHERE K=B (0) 1IS THE CLOSED UNIT BALL OF A. WE INVESTIGATE AND CHARACTERIZE SOME BASIC PROPERTIES, SUCH AS IDEMPOTENT ELEMENTS, NILPOTENT ELEMENTS AND BOUNDED APPROXIMATE IDENTITIES OF THE BANACH FUNCTION ALGEBRA CJ (K). FINALLY WE CHARACTERIZE SOME ELEMENTS OF THE CHARACTER SPACE D (CJ(K)).

IN THIS PAPER, THE HAAR WAVELETS IS APPLIED TO OBTAIN APPROXIMATE SOLUTIONS OF NONLINEAR MULTI-ORDER FRACTIONAL DIFFERENTIAL EQUATIONS (M-FDES). THE FRACTIONAL DERIVATIVE IS DESCRIBED IN THE CAPUTO SENSE.NUMERICAL EXAMPLE IS PRESENTED TO VERIFY THE EFFICIENCY AND ACCURACY OF THE PROPOSED ALGORITHM. THE RESULTS REVEAL THAT THE METHOD IS ACCURATE AND EASY TO IMPLEMENT.

LET A AND B BE TWO BANACH ALGEBRAS, M BE A BANACH (A, B) -MODULE AND N BE A BANACH (B,A) -MODULE.IN THIS PAPER, WE FIRST INTRODUCE THE CONCEPT OF GENERALIZED MATRIX BANACH ALGEBRAS OF ORDER 2 DENOTED BY (FORMULA) THEN WE PRESENT SOME RESULTS CLARIFYING THE RELATION BETWEEN N-WEAK AMENABILITY OF G AND THAT OF A AND B. OUR RESULTS IMPROVE SOME RESULTS IN THE LITERATURE.

IN THIS PAPER WE INVESTIGATE WAVELET COLLOCATION-FINITE DIFFERENCE METHOD FOR SOLVING TWO-DIMENSIONAL MODEL OF DRUG RELEASE IN THE CARDIOVASCULAR TISSUE FROM THE STENT.

LET A AND X BE BANACH ALGEBRAS AND LET X BE AN ALGEBRAIC BANACH A-MODULE. THEN THE L1-DIRECT SUM AX EQUIPPED WITH THE MULTIPLICATION (FORMULA) IS A BANACH ALGEBRA, WHICH WE DENOTE IT BY A¥ X. MODULE EXTENSION ALGEBRAS, LAU PRODUCT AND ALSO THE DIRECT SUM OF BANACH ALGEBRAS ARE THE MAIN EXAMPLES SATISFYING THIS FRAMEWORK. I THIS NOTE WE INVESTIGATE THE CYCLIC AMENABILITY OF A¥ X. WE THEN APPLY THE RESULTS TO THE SPECIAL CASES TO IMPROVE SOME OLDER RESULTS.

LET P BE A PROJECTIVE UNITARY REPRESENTATION OF A DISCRETE COUNTABLE ABELIAN GROUP G ON A SEPARABLE HILBERT SPACE WHICH IS ASSOCIATED TO A CYCLIC GENERALIZED FRAME MULTIRE SOLUTION ANALYSIS. WE USE STONE′S THEOREM AND THE THEORY OF PROJECTION VALUED MEASURE TO ANALYZE WANDERING FRAME COLLECTIONS. THIS YIELDS A FUNCTIONAL ANALYTIC METHOD OF CONSTRUCTING A WAVELET FROM A GENERALIZED FRAME MULTIRESOLUTION ANALYSIS IN TERM OF THE FRAME SCALING VECTORS. IF THE SET BP OF BESSEL VECTORS FOR P IS DENSE IN H, THEN FOR ANY VECTOR XÎ H THE ANALYSIS OPERATOR QX MAKES SENSE AS A DENSELY DEFINED OPERATOR FROM BP TO L2 (G) -SPACE.

IN THIS PAPER WE SEEK SOME CONDITIONS UNDER WHICH PROXIMINALITY OF A SET CAN BE OBTAINED. THEN WE SHOW THAT, AS AN EXAMPLE OF OUR RESULTS, THE SET OF CONSTANT POLYNOMIALS IS PROXIMINAL INC [0,1].

CONSIDER THE WAVE PACKET GROUP (FORMULA) WHERE H AND K ARE LOCALLY COMPACT GROUPS, K IS ALSO ABELIAN AND (FORMULA) IS A CONTINUOUS HOMOMORPHISM. IN THIS ARTICLE, WE EXTEND THE NOTATION OF ZAK TRANSFORM ON L2 (GQ) AND INTRODUCE A FRAME CONDITION TO GENERATE WAVE PACKET FRAMES ON GQ.

IN THIS PAPER, WE INTRODUCE THE CONCEPT OFK-FUSION FRAMES AND PROPOSE THE DUALITY FOR SUCH FRAMES. THE RELATION BETWEEN THE LOCAL FRAMES OFK-FUSION FRAMES WITH THEIR DUAL IS STUDIED. THE ELEMENTS FROM THE RANGE OF A BOUNDED LINEAR OPERATORK CAN BE RECONSTRUCTED BY K-FRAMES. ALSO, WE ESTABLISH K-FUSION FRAME MULTIPLIERS AND INVESTIGATE RECONSTRUCTION OF THE RANGE OFK BY THEM.

IN THIS PAPER WE CHARACTRIZE PARSEVAL ADMISSIBLE VECTORS IN L2 (K), WHERER K IS A LOCALLY COMPACT HYPERGROUP.

IN THIS PAPER, WE ARE GOING TO DEFINE AND STUDY THE DRAZIN AND MOORE-PENROSE SPECTRUM AND OBTAIN SOME RESULT FOR DRAZIN AND MOORE-PENROSE INVERSE.

IN THIS ARTICLE, A REVIEW ON DEFINITION OF THEX - RAY TRANSFORM IS PRESENTED. WE SHALL SHOW THAT THE X -RAY TRANSFORM IS A SPECIAL CASE OF THE RADON TRANSFORM ON HOMOGENEOUS SPACES WHEN THE TOPOLOGICAL GROUPE (N) -THE EUCLIDEAN GROUP- ACTS ON R2 TRANSITIVELY. THEN ITS APPLICATION IN CRYSTALLOGRAPHY IS BRIEFLY STUDIED.

IN THIS TALK, FOR A LOCALLY COMPACT GROUPG, P Î (1; +¥) AND Q Î [1; +¥), WE ARE INTERESTED TO FIND WHEN THE RELATION LP (G) * LQ (G) Í LQ(G) HOLDS. FOR THIS, WE DETERMINE THE TOPOLOGICAL SIZE OF THE SET (F. G) Î LP (G)´ LQ (G): F * G Î LQ (G) |WHEN G IS A NON-COMPACT LOCALLY COMPACT AMENABLE GROUP.

IN THIS PAPER, WE PRESENT SOME RESULTS CONCERNING DERIVATIONS AND JORDAN DERIVATIONS ON THE NONCOM MUTATIVE BANACH ALGEBRA L¥ (G)*. WE SHOW THAT THE RANGE OF ANY (SKEW-) CENTRALIZING DERIVATION ON L¥ (G)* IS EMBEDDED INTO M (L¥, C (G)), AND THE ZERO MAP IS THE ONLY SKEW-COMMUTING DERIVATION ON L¥ (G)*. WE ALSO PROVE THAT THE SUBSPACE ANNR (L¥ (G)*) OF L¥ (G)* IS INVARIANT UNDER JORDAN DERIVATIONS.

K-FRAMES, AS A NEW GENERALIZATION OF FRAMES WHICH WERE RECENTLY INTRODUCED BY GAVRU TA IN HILBERT SPACES.THEY ARE MORE GENERAL THAN FRAMES IN THE SENCE THAT THE LOWER FRAME BOUND ONLY HOLDS FOR THE ELEMENTS IN THE RANG OF K, WHERE K IS A BOUNDED LINEAR OPERATOR IN A SEPARABLE HILBERT SPACE H. MANY PROPERTIES FOR FRAMES MAY NOT HOLD FOR K -FRAMES. IN THIS PAPER WE WILL DISCUSS SOME DI ERENCES BETWEEN K -FRAMES AND FRAMES.

WE STUDY IDEMPOTENT STATES ON LOCALLY COMPACT QUANTUM GROUPS AND ITS DUAL QUANTUM GROUPS AND FIGURE OUT THEIR RELATIONS WITH QUANTUM SUBGROUPS. WE ESTABLISH A ONE TO ONE CORRESPONDENCE BETWEEN IDEMPOTENT STATES ON A LOCALLY COMPACT QUANTUM GROUPS G AND INTEGRABLE COIDEAL VON NEUMANN SUBALGEBRAS OF L¥ (G) THAT ARE PRESERVED BY THE SCALING GROUP. WE ALSO ESTABLISH A ONE TO ONE CORRESPONDENCE BETWEEN OPEN QUANTUM SUBGROUPS OF G AND CENTRAL IDEMPOTENT STATES ON THE DUAL QUANTUM GROUP G.

IN THIS PAPER WE CONSIDER TWO FAMILIES OF FOUR OR FIVE-DIMENSIONAL SOLVABLE LIE GROUPS WHICH ARE EXTENSIONS OF THE HEISENBERG GROUP. WE FIRST CALCULATE THE ENERGY OF AN ARBITRARY LEFT-INVARIANT VECTOR FIELDX ON THESE SPACES. THEN WE OBTAIN THE EXACT FORM OF ALL HARMONIC MAPS ON THESE SPACES AND PROVE THAT IF THESE SPACES ADMIT A NON-TRIVIAL HARMONIC MAP, THEN ANY HARMONIC MAP IS A CRITICAL POINT FOR THE ENERGY FUNCTIONAL RESTRICTED TO VECTOR FIELDS OF THE SAME LENGTH. LATER ON, WE INVESTIGATE THE EXISTENCE OF LEFT-INVARIANT YAMABE SOLITONS AND EXPLICITLY DESCRIBE ALL GEODESIC VECTORS ON THESE SPACES.

FOR A LOCALLY COMPACT GROUP G AND TWO CLOSED SUBGROUPS H, N OF G, WE ARE GOING TO WRITE MG/H AS THE INTEGRAL, WITH RESPECT TO MG/N OF A FAMILY OF MEASURES ON G=H INDEXED BY THE POINTS OF G=N, IN WHICH MG/H AND MG/N ARE MEASURES ON QUOTIENT SPACES G/H AND G/N, RESPECTIVELY.

FOR A LAU ALGEBRA A WITH A CERTAIN CONDITION WE SHOW THAT THE NUMBER OF TOPOLOGICALLY LEFT INVARIANT MEANS ON A* IS EQUAL TO THE NUMBER OF TOPOLOGICALLY LEFT INVARIANT MEANS ON LUC (A*). USING THIS FOR A NONDISCRETE LOCALLY COMAPCT GROUP G WE PROVE THAT THE CARDINALITY OF THE SET OF TOPOLOGICALLY INVARIANT MEANS ON UC (G) IS EQUAL TO 22B (G). IN PARTICULAR, G IS DISCRETE IF AND ONLY IF THERE IS A UNIQUE TOPOLOGICALLY INVARIANT MEAN ON UC (G).

IN THIS PAPER WE INTRODUCE THE TERMS OF TRIPLE APPROXIMATE IDENTITY AND TERNARY AMENABILITY FOR JB* TRIPLE SYSTEMS AND THEN WE SHOW THAT EVERY TERNARY AMENABLE COMMUTATIVE JB* TRIPLE SYSTEM POSSESSES AN TRIPLE APPROXIMATE IDENTITY.

IT IS NECESSARY IN THE FRAMEWORK OF NUMERICAL ANALYSIS TO BE A LOT OF MORE CAREFUL FIRST OF ALL ABOUT THE CHOICE OF SPACE OF FUNCTIONS X TO WHICH THE SOLUTION BELONGS. IN THIS WORK, WE INTRODUCE SOME USEFUL SPACES FOR EXAMPLE THE ORLICZ, LORENTZ AND LP,A SPACES. FINALLY SOME PROPERTIES OF THESE SPACES ARE STATED.

WE WILL SHOW THAT EVERY KC-FUNCTION F: X´Y® Z IS STRONGLY QUASI-CONTINUOUS PROVIDED THAT X IS BAIRE, Y A W-SPACE AND Z IS REGULAR. IT FOLLOWS THAT IF Y IS A MOORE W-SPACE AND G IS A BAIRE LEFT TOPOLOGICAL GROUP, THEN EVERY KC-ACTION P: G´ Y® Y IS JOINTLY CONTINUOUS. OUR RESULTS ENABLE US TO OBTAIN CONDITIONS WHICH IMPLY THAT A SEMITOPOLOGICAL GROUP IS AUTOMATICALLY A PARATOPOLOGICAL.

IN NUMERICAL ANALYSIS SPECIALLY IN FINDING NUMERICAL SOLUTION FOR PDES AND INTEGRAL EQUATIONS, DIFFERENT BASIS FUNCTIONS ARE USED. FRAMES HAVE NOT BEEN USED IN THE MENTIONED METHODS, BECAUSE OF THE LACK OF INDEPENDENCY BETWEEN THEIR ELEMENTS. IN THIS PAPER, FIRST WE INTRODUCE A SHEARLET FRAME THEN WE EXTRACT A FINITE BASIS FROM IT.

THE DUAL OF AN INTROVERTED SUBSPACE OF THE DUAL OF A BANACH ALGEBRA ENJOYS TWO (ARENS TYPE) PRODUCTS. IN THIS TALK WE INVESTIGATE THE TOPOLOGICAL CENTERS RELATED TO THESE PRODUCTS FOR A GENERAL INTROVERTED SUBSPACE.SOME OLDER RESULTS ON CERTAIN INTROVERTED SUBSPACES OF L¥ (G) ARE EXTENDED TO A GENERAL INTROVERTED SUBSPACE.

LET A BE A BANACH ALGEBRA AND X BE AN ARBITRARY BANACH A -BIMODULE. IN THIS PAPER, WE STUDY SECOND TRANSPOSE A DERIVATION WITH VALUE IN DUAL BANACH A -MODULE X*: INDEED, FOR A CONTINUOUS DERIVATION D: A®X* WE OBTAIN A NECESSARY AND SUFFICIENT CONDITION SUCH THAT THE BOUNDED LINEAR MAP Ù O D”: A ** ®X *** TO BE A DERIVATION, WHERE Ù IS COMPOSITION OF RESTRICTION AND CANONICAL INJECTION MAPS.

LET A BE A BANACH ALGEBRA, S AND T ARE LINEAR MAPPINGS (OR HOMOMORPHISMS) ON BANACH ALGEBRAA. A LINEAR MAP D: A®A IS CALLED (S,T) -DERIVATION IF (FORMULA) A LINEAR MAPPING: A®A IS CALLED A (S,T) -DERIVATION IF THERE EXISTS A (S,T) –DERIVATION D: A®A SUCH THAT (FORMULA) IN THIS TALK, WE INVESTIGATE AUTOMATIC CONTINUITY OF THESE DERIVATIONS ON BANACH ALGEBRAS.

IN THIS TALK WE PRESENT SOME RECENT RESULTS ON ZERO PRESERVING MAPS ON CERTAIN BANACH ALGEBRAS, INCLUDING C*-ALGEBRAS, GROUP CONVOLUTION ALGEBRAS, MATRIX LIKE ALGEBRAS, ETC.

FOR A BANACH ALGEBRA A THE STRICT TOPOLOGY ON A IS DEFINED AS THE LOCALLY CONVEX TOPOLOGY ON A INDUCED BY THE FAMILY OF SEMINORMS {LA, A Î A}, WHERE LA (B) =||AB||, FOR ALL B 2 A. BY THE NORM-STRICT BIDUAL OF A WE MEAN THE NORM DUAL OF THE SPACE (A,B) *. IN THIS PAPER, AMONG OTHER THINGS, WE INVESTIGATE THE CONTINUITY PROPERTIES OF THE PRODUCT ON ((A,B)*,||.||) *, FOR SOME SPECIAL BANACH ALGEBRAS. IN PARTICULAR, GENERALIZING SOME RESULTS OF M. NEUFANG, WE SHOW THAT IF B IS A NORM BOUNDED SUBSET OF<A*A>, AND IFM0 Î RM (A), THE RIGHT MULTIPLIER ALGEBRA OF A, AND N0 ÎB, THEN THE MAPPING (M, N)®M. N FROM< A*A>´B INTO<A*A>IS JOINTLY CONTINUOUS AT (M0,N0) IN THE UEB- TOPOLOGY, THAT IS THE TOPOLOGY OF UNIFORM CONVERGENCE ON EQUICONTINUOUS BOUNDED SUBSETS OF<A*A>.

IN THIS PAPER, A NEW METHOD BASED ON THE BERNOULLI WAVELETS EXPANSION TOGETHER WITH OPERATIONAL MATRIX OF FRACTIONAL INTEGRATION IS PROPOSED TO SOLVE TIME-FRACTIONAL PARTIAL DI ERENTIAL EQUATIONS. THE PROPOSED METHOD IS VERY CONVENIENT FOR SOLVING SUCH PROBLEMS, SINCE THE INITIAL AND BOUNDARY CONDITIONS ARE TAKEN INTO ACCOUNT AUTOMATICALLY. THE SUGGESTED METHOD REDUCES THIS TYPE OF EQUATION TO THE SOLUTION OF A ALGEBRAIC SYSTEM. THEY HAVE BEEN USED IN MODELING TURBULENT FLOW CHAOTIC DYNAMICS OF CLASSICAL CONSERVATION SYSTEMS.

IN THIS PAPER, WE EXTENDS THE CONTINUOS WAVELET TRANSFORM ON SPHERE, WHICH THE FOUNDATION OF BUILDING WAVELET ON EACH MANIFOLD IS BASED ON GROUP THEORETICAL APPROACH. IN THIS TECHNIQUE, WAVELETS ARE CONSIDERED AS AN ORDERED POSITIONS RELATED TO GROUP THEORETICAL.

IN THIS TALK WE INVESTIGATE CONTRACTIBILITY OF NON-ARCHIMEDEAN BANACH ALGEBRAS.

ERROR ESTIMATE AND THE RATE OF CONVERGENCE ARE VERY IMPORTANT IN THE FRAMEWORK OF NUMERICAL ANALYSIS.WITHOUT DOUBT HAVING ENOUGH INFORMATION OF THE MOST IMPORTANT INEQUALITIES PLAY AN IMPORTANT ROLE IN ACHIEVING BETTER BOUND IN NUMERICAL ALGORITHMS. THIS PAPER FOCUSES ON HARDY’S INEQUALITY ASSOCIATED WITH THE JACOBI WEIGHT FUNCTION (FORMULA).

ERROR ESTIMATE AND THE RATE OF CONVERGENCE ARE VERY IMPORTANT IN THE FRAMEWORK OF NUMERICAL ANALYSIS.WITHOUT DOUBT HAVING ENOUGH INFORMATION OF THE MOST IMPORTANT INEQUALITIES PLAY AN IMPORTANT ROLE IN ACHIEVING BETTER BOUND IN NUMERICAL ALGORITHMS. THIS PAPER FOCUSES ON HARDY’S INEQUALITY ASSOCIATED WITH THE JACOBI WEIGHT FUNCTION (FORMULA).

IN THIS PAPER, WE PRESENT A CHARACTERIZATION OF THE CLOSED IDEAL OF A TRIVOLUTIVE BANACH ALGEBRA (A,T).THE MAIN RESULTS ARE: A) THE CLOSED IDEAL I=KER T OF A UNITAL BANACH ALGEBRA A IS PRINCIPLE. B) FOR A COMMUTATIVE TRIVOLUTIVE ALGEBRA A, THERE IS AN IDEMPOTENT UÎA** SUCH THAT KER T =IU IN WHICH IU={A Î A; AU=0}. AFTER THAT WE INVESTIGATE TRIVOLUTIONS ON THE FOURIER-STIELTJES ALGEBRA B (G): MOREOVER, WE STUDY TRIVOLUTIONS ON THE ALGEBRA A´QB WITH Q-LAU PRODUCT IN RELATION TO THE CORRESPONDING ONE OF A AND B.

IN THIS PAPER WE INTRODUCE A CLASS OF CONTINUOUS FRAMES IN A HILBERT SPACE H WHICH IS INDEXED BY SOME LOCALLY COMPACT GROUP G, EQUIPPED WITH ITS LEFT HAAR MEASURE. THESE FRAMES ARE OBTAINED AS THE ORBITS OF A SINGLE ELEMENT OF HILBERT SPACE H UNDER SOME UNITARY REPRESENTATION P OF G ON H.

FRAMES IN HILBERT SPACES ARE A REDUNDANT OF VECTORES WHICH YIELD A REPRESENTATION FOR EACH VECTOR IN THE SPACE.K -FRAMES WERE RECENTLY INTRODUCED BY GAVRUTA IN HILBERT SPACES. THEY RESPECT TO A BOUNDED LINEAR OPERATORK. IN THIS PAPER, WE WILL PRESENT SOME CONDITIONS OF UNIQUENESS DUAL FRAME AND DUAL K -FRAME IN CASES.

HIGHER DIMENSIONAL ANALOGS OF THE CLASSICAL CONTINUOUS WAVELET TRANSFORM ARE DEVELOPED FOR EUCLIDEAN SPACES WHOSE DIMENSION IS A PERFECT SQUARE. THE SPACE OF ALL N´N REAL MATRICES CAN BE IDENTIFIED WITH RN2 AS AN ADDITIVE ABELIAN GROUP. THE GROUP OF INVERTIBLE N´N REAL MATRICES NATURALLY ACTS ON THIS ABELIAN GROUP BY MATRIX MULTIPLICATION. THE RESULTING SEMI DIRECT PRODUCT GROUP FORMS A GROUP OF AFFINE TRANSFORMATIONS OF R N2 WHICH MAY BE VIEWED AS A GENERALIZATION OF THE AFFINE TRANSFORMATIONS OF R N2 WHOSE UNIQUE SQUARE-INTEGRABLE REPRESENTATION UNDERLIES THE CLASSICAL ONE-DIMENSIONAL CONTINUOUS WAVELET TRANSFORM. A CONTINUOUS WAVELET TRANSFORM FOR R N2 IS DERIVED AND ITS SPECIFIC DETAILS ARE WORKED OUT FOR R 4 RESULTING IN A 4D CONTINUOUS WAVELET TRANSFORM. WE PROVIDE THREE EQUIVALENT VERSIONS OF THE IRREDUCIBLE REPRESENTATION OF G=A H FOR A=M (N, R) AND H=GL (N, R) UNDERLIES THE CONTINUOUS WAVELET TRANSFORM AND THEN THREE VERSIONS OF THE IRREDUCIBLE REPRESENTATION OF G=A⋊H SUCH THAT A IS LOCALLY COMPACT ABELIAN GROUP AND H IS LOCALLY COMPACT GROUP.

WE ESTABLISH SOME INEQUALITIES FOR MARTINGALES IN THE FRAMEWORK OF NONCOMMUTATIVE PROBABILITY SPACES.

LET F: X´Y® Z BE A BILINEAR MAPPING ON NORMED SPACES. IN THIS PAPER WE INVESTIGATE THAT ARE THE TOPOLOGICAL CENTERS OFF, W*-DENSE IN THE CORRESPONDING TOPOLOGICAL CENTERS OF ITS EXTENSIONS F *** AND FT***T? WE SHOW THAT ALTHOUGH IT HAS POSITIVE ANSWER ON SOME SPECIAL CASES BUT THIS IS NOT TRUE IN GENERAL.

LET TK DENOTE TRANSLATION BY KÎZD . GIVEN COUNTABLE COLLECTIONS OF FUNCTIONS (FORMULA) AND ASSUMING THAT (FORMULA) ARE BESSEL SEQUENCES, WE ARE INTERESTED IN EXPANSIONS (FORMULA) OUR MAIN RESULT GIVES AN EQUIVALENT CONDITION FOR THIS TO HOLD IN A MORE GENERAL SETTING THAN DESCRIBED HERE, WHERE TRANSLATION BY K ÎZD IS REPLACED BY TRANSLATION VIA THE ACTION OF A MATRIX. AS SPECIAL CASES OF OUR RESULT WE FIND CONDITIONS FOR SHIFT-INVARIANT SYSTEMS TO GENERATE A SUBSPACE FRAME WITH A CORRESPONDING DUAL HAVING THE SAME STRUCTURE. IN THIS PAPER WE CONSIDER THE IMPORTANT CASE OF GENERALIZED SHIFT-INVARIANT SYSTEMS AND PROVIDE VARIOUS WAYS OF ESTIMATING THE DEVIATION FROM PERFECT RECONSTRUCTION THAT OCCUR WHEN THE SYSTEMS DO NOT FORM DUAL FRAMES. THE DEVIATION FROM BEING DUAL FRAMES WILL BE MEASURED EITHER IN TERMS OF A PERTURBATION CONDITION OR IN TERMS OF THE DEVIATION FROM EQUALITY IN THE DUALITY CONDITIONS.

REPRODUCING KERNEL HILBERT SPACES ARISE IN A NUMBER OF AREAS, INCLUDING APPROXIMATION THEORYS STATISTICS, MACHINE LEARNING THEORY, GROUP REPRESENTATION THEORY AND VARIOUS AREAS OF COMPLEX ANALYSIS. IN THIS TALK THE REPRODUCING KERNEL HILBERT SPACES ARE INTRODUCED AND THEIR GENERAL PROPERTIES ARE INVESTIGATED.FOR BETTER UNDERSTANDING OF THESE SPACES SOME EXAMPLES ARE GIVEN. MOREOVER, IN THIS SPACE, A SAMPLING FORMULA IS INTRODUCED, WHICH IS AN EXTENSION OF A FAMOUS FORMULA KNOWN AS THE PALEY-WIENER (PW) OF BAND-LIMITED SIGNALS. IN PARTICULAR, A SINGLE CHANNEL SAMPLING FORMULA IS DISCUSSED.

IN THIS PAPER, A GALERKIN METHOD BASED ON THE SECOND KIND CHEBYSHEV WAVELETS (SKCWS) IS PROPOSED FOR SOLVING A CLASS OF FRACTIONAL PARTIAL INTEGRO-DI ERENTIAL EQUATIONS WITH WEAKLY SINGULAR KERNELS. IN THE PROPOSED METHOD, THE OPERATIONAL MATRIX OF FRACTIONAL ORDER INTEGRATION (OMFI) FOR SKCWS IS USED TO TRANSFORM THE PROBLEM UNDER CONSIDERATION TO A LINEAR SYSTEM OF ALGEBRAIC EQUATIONS WHICH CAN BE SIMPLY SOLVED.