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Note About Office Hours: I encourage you to come by my office if you have any questions, need help with homework problems, or would just like to talk about the material. To make an appointment, send me an email. Course Description: This course provides an introduction to the methods and language of functional analysis, including Hilbert spaces, Banach(More)
Learning Objectives Students learn about the complex number system, metric spaces and the topology of C, elementary properties of analytic functions, conformal mappings, complex integration (including variations of Cauchy's Theorem and the Cauchy Integral Theorem) and singularities of analytic functions Assessment of Learning Outcomes Assessment will be(More)
Learning Objectives Students learn about the complex number system, metric spaces and the topology of C, elementary properties of analytic functions, conformal mappings, complex integration (including variations of Cauchy's Theorem and the Cauchy Integral Theorem) and singularities of analytic functions Assessment of Learning Outcomes Assessment will be(More)
This paper is a contribution to the problem of approximating continuous functions F defined on a compact HausdorfF space X, where the value F(x) is a compact convex set in R" for every x in X. More specifically we show how to transfer Korovkin type approximation theorems for real-valued continuous functions to this set-valued situation. 1. Introduction. We(More)
A version of a theorem commonly referred to as Caristi's Theorem is given. It has an elementary constructive proof and it includes many generalizations of Banach's fixed point theorem. Several examples illustrate the diversity that can occur. X is a complete metric space and 4> is lower semicontinuous. If for each x in X, (C) d(x,Tx) <(p(x)-4>(Tx), then T(More)
Suppose A is a C*-algebra and B is a Banach algebra such that it can be continuously imbedded in B(H), the Banach algebra of bounded linear operators on some Hubert space H. It is shown that if 6 is a compact algebra homomorphism from A into B, then 6 is a finite rank operator, and the range of 0 is spanned by a finite number of idempotents. If, moreover, B(More)
There exists a large number of elementary books on complex function theory because the subject is taught at all universities and engineering schools. In addition there are many research monographs treating selected topics from complex analysis. The present list is only a small selection in addition to the 3 books mentioned in the introduction.