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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.

spaces is open), and the Hahn{Banach Theorem (a bounded linear func-tional on a linear subspace of a normed vector space extends to a bounded linear functional on the entire normed vector space). An equivalent formu-lation of the Open Mapping Theorem is the Closed Graph Theorem (a linear

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FUNCTIONAL ANALYSIS - ETH Z

people.math.ethz.ch

§5.3. Operators on Hilbert Spaces 222 §5.4. Functional Calculus for Self-Adjoint Operators 234 §5.5. Gelfand Spectrum and Normal Operators 246 §5.6. Spectral Measures 261 §5.7. Cyclic Vectors 281 §5.8. Problems 288 Chapter 6. Unbounded Operators 295 §6.1. Unbounded Operators on Banach Spaces 295 §6.2. The Dual of an Unbounded Operator ...

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INTRODUCTION TO DIFFERENTIAL TOPOLOGY

people.math.ethz.ch

INTRODUCTION TO DIFFERENTIAL TOPOLOGY Joel W. Robbin UW Madison Dietmar A. Salamon ETH Zuric h 14 August 2018. ii. ... is the foundational chapter about smooth manifolds in [21] as well as some basic results about geodesics and the exponential map. For the bene t of the reader we summarize some of the relevant background material in the rst ...

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INTRODUCTION TO DIFFERENTIAL GEOMETRY

people.math.ethz.ch

One can distinguish extrinsic di erential geometry and intrinsic di er-ential geometry. The former restricts attention to submanifolds of Euclidean space while the latter studies manifolds equipped with a Riemannian metric. The extrinsic theory is more accessible because we …

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Lectures on Symplectic Geometry - ETH Z

people.math.ethz.ch

and their symplectic submanifolds, and in the work of Taubes in the context of the Seiberg-Witten invariants. Symplectic geometry is significantly stimulated by important interactions with global analysis, mathematical physics, low-dimensional topology, dynamical systems, algebraic geometry, integrable systems, microlocal

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