This text introduces students to Hilbert space and bounded self-adjoint operators, as well as the spectrum of an operator and its spectral decomposition. The author, Emeritus Professor of Mathematics at the University of Innsbruck, Austria, has ensured that the treatment is accessible to readers with no further background than a familiarity with analysis and analytic geometry.
Starting with a definition of Hilbert space and its geometry, the text explores the general theory of bounded linear operators, the spectral analysis of compact linear operators, and unbounded self-adjoint operators. Extensive appendixes offer supplemental information on the graph of a linear operator and the Riemann-Stieltjes and Lebesgue integration.

Contenuti

I. The concept of Hilbert space II. Specific geometry of Hilbert space III. Bounded linear operators IV. General theory of linear operators V. Spectral analysis of compact linear operators VI. Spectral analysis of bounded linear operators VII. Spectral analysis of unbounded selfadjoint operators Appendix A. The graph of a linear operator Appendix B. Riemann-Stieltjes and Lebesgue integration Bibliography Index of symbols Subject index

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