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Sampling Integrodifferential Transforms Arising from Second Order Differential Operators
Author(s) -
Annaby Mahmoud H.,
Freiling Gerhard
Publication year - 2000
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/1522-2616(200008)216:1<25::aid-mana25>3.0.co;2-v
Subject(s) - mathematics , class (philosophy) , sampling (signal processing) , eigenvalues and eigenvectors , boundary value problem , order (exchange) , mathematical analysis , differential equation , function (biology) , differential (mechanical device) , pure mathematics , physics , filter (signal processing) , finance , quantum mechanics , artificial intelligence , evolutionary biology , computer science , economics , computer vision , biology , engineering , aerospace engineering
We give sampling theorems associated with boundary value problems whose differential equations are of the form M ( y ) = λ S ( y ), where M and S are differential expressions of the second and first order respectively and the eigenvalue parameter may appear in the boundary conditions. The class of the sampled functions is not a class of integral transforms as is the case in the classical sampling theory, but it is a class of integrodifferential transforms. We use solutions of the problem as well as Green's function to derive two sampling theorems.