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Compact Operators. Equations with Compact Operators

Yu. M. Berezansky, Zinovij G. Sheftel, Georgij F. Us

Abstract

In this chapter, we study an important class of linear continuous operators, namely, compact (or completely continuous) operators. On the one hand, compact operators are interesting because they inherit many properties of operators in finite-dimensional spaces. On the other hand, many operators important for applications are compact; in particular, this is true for integral operators with “sufficiently good” kernels.

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Available abstract

Key concepts: Compact operator on Hilbert space, Operator theory, Nuclear operator, Fourier integral operator, Compact operator, Spectral theorem, Mathematics, Operator norm