Titlebook: Real and Functional Analysis; Vladimir I. Bogachev,Oleg G. Smolyanov Textbook 2020 Springer Nature Switzerland AG 2020 meromorphic functio

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https://doi.org/10.1007/978-3-030-38219-3meromorphic functions; Riemann theorem; harmonic functions; Fuchsian groups; Riemann surfaces; moduli of

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978-3-030-38221-6Springer Nature Switzerland AG 2020

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Unbounded Operators and Operator Semigroups,ps. Some of the principal applications of these theories are connected with partial differential equations and mathematical physics, in particular, quantum mechanics, but there are also important applications in many other areas of mathematics, for example, in the theory of random processes and geometry.

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Banach Algebras,hysics. One of the most important Banach algebras is the algebra of operators. Considerations of this chapter shed a new light on some already encountered objects and also complement some results obtained above.

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Metric and Topological Spaces,In this chapter we consider the most important concepts of modern analysis — metric and topological spaces. Large parts of the chapter consist of definitions and examples (probably, already familiar to the reader from a course of calculus), moreover, some additional information about compact spaces needed for the sequel is given.

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Fundamentals of Measure Theory,In this chapter and the next two we present Lebesgue’s theory of measure and integral. In addition, we discuss connections between integration and differentiation.