FUNCTIONAL ANALYSIS - People

FUNCTIONAL ANALYSISTheo B uhlerETH Z urichDietmar A. SalamonETH Z urich8 June 2017iiPrefaceThese are notes for the lecture course FUNCTIONAL ANALYSIS I held by thesecond author at ETH Z urich in the fall semester 2015. Prerequisites arethe first year courses onAnalysisandLinear Algebra, and the second yearcourses onComplex ANALYSIS ,Topology, andMeasure and material of Subsection on elementary Hilbert space theory, Sub-section on the Stone Weierstra Theorem, and the appendices on theLemma of Zorn and Tychonoff s Theorem has not been covered in the lec-tures. These topics were assumed to have been covered in previous lecturecourses. They are included here for completeness of the material of Subsection on the James space, Section on thefunctional calculus for bounded normal operators, Chapter 6 on unboundedlinear operators, Subsection on Banach space valuedLpfunctions, Sub-section on self-adjoint and unitary semigroups, and Section on an-alytic semigroups was not part of the lecture course (with the exception ofsome of the basic definitions in Chapter 6 that are relevant for infinitesimalgenerators)

functional analysis for many of the relevant applications. The manuscript is addressed primarily to third year students of mathe-matics or physics, and the reader is assumed to be familiar with rst year analysis and linear algebra, as well as complex analysis and the basics of point set topology and measure and integration.

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  Analysis, Physics, Functional, Complex, Functional analysis, Complex analysis

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