IN THIS TALK WE STATE THAT Linear DYNAMICAL SYSTEMS HAVING LIMIT SHADOWING property OR AVERAGE SHADOWING property ARE HYPERBOLIC.

ONE OF THE OLDEST AND MOST COMMON DISEASES IN THE WORLD IS TUBERCULOSIS WHICH CAN BE CAUSED BY THE MYCOBACTERIUM TUBERCULOSIS. ABOUT ONE THIRD OF THE WORLD'S POPULATION ARE INFECTED BY THIS BACTERIUM, WHICH LEADS TO DEATH OF 2-2.5 MILLION PEOPLE EACH YEAR. …

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.

THIS PAPER IS DEVOTED TO THE STUDY OF reproducing KERNEL HILBERT SPACES. WE FOCUS ON MULTIPLIERS OF reproducing KERNELBANACH AND HILBERT SPACES. IN PARTICULAR WE TRIED TO EXTEND THISCONCEPT AND PROVE SOME THEOREMS.