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Information Journal Paper

Title

SHIFT INVARIANT SPACES AND SHIFT PRESERVING OPERATORS ON LOCALLY COMPACT ABELIAN GROUPS

Pages

  21-32

Abstract

 We investigate shift invariant subspaces of L2 (G), where G is a LOCALLY COMPACT ABELIAN GROUP. We show that every SHIFT INVARIANT SPACE can be decomposed as an orthogonal sum of spaces each of which is generated by a single function whose shifts form a Parseval FRAME. For a second countable LOCALLY COMPACT ABELIAN GROUP G we prove a useful Hilbert space isomorphism, introduce RANGE FUNCTIONs and give a characterization of shift invariant subspaces of L2 (G) in terms of RANGE FUNCTIONs. Finally, we investigate SHIFT PRESERVING OPERATORs on LOCALLY COMPACT ABELIAN GROUPs. We show that there is a one-to-one correspondence between SHIFT PRESERVING OPERATORs and RANGE OPERATORs on L2 (G) where Gis a LOCALLY COMPACT ABELIAN GROUP.

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    APA: Copy

    RAISI TOUSI, R., & KAMYABI GOL, R.A.. (2011). SHIFT INVARIANT SPACES AND SHIFT PRESERVING OPERATORS ON LOCALLY COMPACT ABELIAN GROUPS. IRANIAN JOURNAL OF MATHEMATICAL SCIENCES AND INFORMATICS (IJMSI), 6(2), 21-32. SID. https://sid.ir/paper/310322/en

    Vancouver: Copy

    RAISI TOUSI R., KAMYABI GOL R.A.. SHIFT INVARIANT SPACES AND SHIFT PRESERVING OPERATORS ON LOCALLY COMPACT ABELIAN GROUPS. IRANIAN JOURNAL OF MATHEMATICAL SCIENCES AND INFORMATICS (IJMSI)[Internet]. 2011;6(2):21-32. Available from: https://sid.ir/paper/310322/en

    IEEE: Copy

    R. RAISI TOUSI, and R.A. KAMYABI GOL, “SHIFT INVARIANT SPACES AND SHIFT PRESERVING OPERATORS ON LOCALLY COMPACT ABELIAN GROUPS,” IRANIAN JOURNAL OF MATHEMATICAL SCIENCES AND INFORMATICS (IJMSI), vol. 6, no. 2, pp. 21–32, 2011, [Online]. Available: https://sid.ir/paper/310322/en

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