Manuscript Title:

A HILBERT SPACE APPLICATION OF SAMPLING

Author:

MUSA SIDDIG, AMANI ELSEID ABUZEID

DOI Number:

DOI:10.5281/zenodo.10029795

Published : 2023-10-20

About the author(s)

1. MUSA SIDDIG - University of Kordofan, Faculty of Science, Department of Mathematics, Sudan.
2. AMANI ELSEID ABUZEID - Department of Mathematics, College of Aldaier, Jazan University, Saudi Arabia.

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Abstract

When a function’s values are located in a separable Hilbert space, it is derived the Whittaker-Shannon- Kotel ′nikov sampling theorem. During a Hilbert space, we employ small frame operators and frames. In turn, this provides us an extension Kramer’s second sampling theorem and helps us grow selection of
theorems related to value at the boundary issues and various formulae for homogeneous integrals.


Keywords

Theorem Of Shannon s Sampling, Approximation And Interpolation In A Hilbert Space, Frame Operators And Frames, Sturm-Liouville Boundary-Value Problem, Fredholm Integral Equations, Green s Function, Cauchy-Schwarz Inequality.