Introduction to Spectral Theory in Hilbert Space

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.

Acest text introduce studentilor in spatiul Hilbert si operatorii autoadjuncti delimitati, precum si spectrul unui operator si descompunerea sa spectrala. Autorul, profesor emerit de matematica de la Universitatea din Innsbruck, Austria, s-a asigurat ca tratamentul este accesibil cititorilor care nu au mai multa experienta decat familiarizarea cu analiza si geometria analitica. Incepand cu o definitie a spatiului Hilbert si geometria acestuia, textul exploreaza teoria generala a operatorilor liniari delimitati, analiza spectrala a operatorilor liniari compacti si a operatorilor autoadjunsi nelimitati.