Titlebook: Explorations in Harmonic Analysis; With Applications to Steven G. Krantz Textbook 2009 Birkhäuser Boston 2009 Fourier analysis.Fourier tran

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https://doi.org/10.1007/978-981-16-9543-8The function theory of several complex variables (SCV) is—obviously—a generalization of the subject of one complex variable. Certainly some of the results in the former subject are inspired by ideas from the latter subject. But SCV really has an entirely new character.

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Ontology and History of Real Analysis,Real analysis as a subject grew out of struggles to understand, and to make rigorous, Newton and Leibniz’s calculus. But its roots wander in all directions—into real analytic function theory, into the analysis of polynomials, into the solution of differential equations.

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Fractional and Singular Integrals,In some vague sense, the collection of all fractional and singular integrals forms a poor man’s version of a classical calculus of pseudodifferential operators. Certainly a fractional integral is very much like the parametrix for a strongly elliptic operator.

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A Crash Course in Several Complex Variables,The function theory of several complex variables (SCV) is—obviously—a generalization of the subject of one complex variable. Certainly some of the results in the former subject are inspired by ideas from the latter subject. But SCV really has an entirely new character.

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Introduction to the Heisenberg Group,This chapter and the next constitute the climax of the present book.We have tried to lay the groundwork so that the reader may see how it is natural to identify the boundary of the unit ball in ℃. with the Heisenberg group and then to do harmonic analysis on that group.

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