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Expansion of a Self-Adjoint Absolutely Continuous Singular Integral Operator in Generalized Eigenvectors and Its Diagonalization

We describe the relationship between the expansion of a self-adjoint operator in generalized eigenvectors and the direct integral of Hilbert spaces. We perform the explicit diagonalization of a self-adjoint absolutely continuous singular integral operator Y using an Hermitian nonnegative kernel cons...

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Bibliographic Details
Date:	2003
Main Authors:	Vorob'ev, I. V., Воробйов, І. В.
Format:	Article
Language:	Ukrainian English
Published:	Institute of Mathematics, NAS of Ukraine 2003
Online Access:	https://umj.imath.kiev.ua/index.php/umj/article/view/3896
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Journal Title:	Ukrains’kyi Matematychnyi Zhurnal
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