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Matrix And Operator Valued Functions by Gohberg%2c I.

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1Time And Band Limiting For Matrix Valued Functions: An Integral And A Commuting Differential Operator

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The problem of recovering a signal of finite duration from a piece of its Fourier transform was solved at Bell Labs in the $1960$'s, by exploiting a "miracle": a certain naturally appearing integral operator commutes with an explicit differential one. Here we show that this same miracle holds in a matrix valued version of the same problem.

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  • Title: ➤  Time And Band Limiting For Matrix Valued Functions: An Integral And A Commuting Differential Operator
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The book is available for download in "texts" format, the size of the file-s is: 0.19 Mbs, the file-s for this book were downloaded 24 times, the file-s went public at Fri Jun 29 2018.

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2Some Examples Of Matrix-valued Orthogonal Functions Having A Differential And An Integral Operator As Eigenfunctions

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The aim of this paper is to show some examples of matrix-valued orthogonal functions on the real line which are simultaneously eigenfunctions of a second-order differential operator of Schr\"{o}dinger type and an integral operator of Fourier type. As a consequence we derive integral representations of these functions as well as other useful structural formulas. Some of these functions are plotted to show the relationship with the Hermite or wave functions.

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  • Title: ➤  Some Examples Of Matrix-valued Orthogonal Functions Having A Differential And An Integral Operator As Eigenfunctions
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  • Language: English

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The book is available for download in "texts" format, the size of the file-s is: 11.23 Mbs, the file-s for this book were downloaded 59 times, the file-s went public at Mon Sep 23 2013.

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