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Eigenvalue and singular value estimates for integral operators: a unifying approach
Author(s) -
Menegatto V. A.,
Oliveira C. P.
Publication year - 2012
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/mana.201100257
Subject(s) - mathematics , multiplier (economics) , singular integral operators , singular integral , eigenvalues and eigenvectors , operator (biology) , smoothness , kernel (algebra) , square integrable function , singular value , mathematical analysis , fourier integral operator , measure (data warehouse) , pure mathematics , operator theory , integral equation , biochemistry , chemistry , physics , repressor , quantum mechanics , database , gene , transcription factor , computer science , economics , macroeconomics
We consider integral operators generated by square integrable kernels on an abstract measure space. Under smoothness assumptions defined by the action of a convenient multiplier‐like operator on the kernel, we deduce decay rates for either the eigenvalues or the singular values of the integral operator. The setting is an abstract framework which encompasses classical cases that have appeared in different sources in the literature.