Titlebook: Basic Classes of Linear Operators; Israel Gohberg,Seymour Goldberg,Marinus A. Kaashoe Textbook 2003 Springer Basel AG 2003 Hilbert space.O

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Karen Blixen und Heinrich Heineperators form important classes of operators and they appear in many applications. They also have remarkable properties. For instance, there are different methods to invert explicitly these operators, and to compute their spectra. This chapter reviews these results starting from the simplest class.

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Friedrich-Wilhelm von Oppeln-Bronikowski the convergence of the finite section method is analyzed. In the proofs factorization is used systematically. The chapter also contains extensions of the theory to pair operators and to a simple class of singular integral operators on the unit circle.

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Non Linear Operators,one of the simplest; the Contraction Mapping Theorem. This theorem is very powerful in that it allows one to prove the existence of solutions to nonlinear integral, differential and functional equations, and it gives a procedure for numerical approximations to the solution. Some of the applications are also included in this chapter.

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aduate or graduate courses on operator theory or functional The present book is an expanded and enriched version ofthe textBasicOperator Theory, written by the first two authors more than twenty years ago. Since then the three ofus have used the basic operator theory text in various courses. This ex

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Der »Schwarze Sascha« und Heineerefore we prove the Hilbert-Schmidt theorem and Mercer’s theorem since each of these theorems gives conditions for a uniform convergence of the spectral decomposition of the integral operators. As a corollary of Mercer’s theorem we obtain the trace formula for positive integral operators with continuous kernel function.

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