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Explorations in Harmonic Analysis: With Applications to Complex Function Theory and the Heisenberg Group - Rilegato
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This self-contained text provides an introduction to modern harmonic analysis in the context in which it is actually applied, in particular, through complex function theory and partial differential equations. It takes the novice mathematical reader from the rudiments of harmonic analysis (Fourier series) to the Fourier transform, pseudodifferential operators, and finally to Heisenberg analysis.
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This self-contained text provides an introduction to modern harmonic analysis in the context in which it is actually applied, in particular, through complex function theory and partial differential equations. It takes the novice mathematical reader from the rudiments of harmonic analysis (Fourier series) to the Fourier transform, pseudodifferential operators, and finally to Heisenberg analysis.
Within the textbook, the new ideas on the Heisenberg group are applied to the study of estimates for both the Szegö and PoissonSzegö integrals on the unit ball in complex space. Thus the main theme of the book is also tied into complex analysis of several variables. With a rigorous but well-paced exposition, this text provides all the necessary background in singular and fractional integrals, as well as Hardy spaces and the function theory of several complex variables, needed to understand Heisenberg analysis.
Explorations in Harmonic Analysis is ideal for graduate students in mathematics, physics, and engineering. Prerequisites include a fundamental background in real and complex analysis and some exposure to functional analysis.
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Explorations in Harmonic Analysis : With Applications to Complex Function Theory and the Heisenberg Group
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Explorations in Harmonic Analysis (Hardcover)
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Birkhauser Boston Inc, Secaucus, 2009
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ISBN 13: 9780817646684
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Hardcover. Condizione: new. Hardcover. Harmonic analysis is a venerable part of modern mathematics. Its roots began, perhaps, with late eighteenth-century discussions of the wave equation. Using the method of separation of variables, it was realized that the equation could be solved with a data function of the form?(x)= sin jx for j? Z.Itwasnaturaltoask, using the philosophy of superposition, whether the equation could then be solved with data on the interval [0,?] consisting of a nite linear combinationof the sin jx. With an af rmative answer to that question, one is led to ask about in?nite linear combinations. This was an interesting venue in which physical reasoning interacted with mathematical reasoning. Physical intuition certainly suggests that any continuous function? can be a data function for the wave equation. So one is led to ask whether any continuous? can be expressed as an (in nite) superposition of sine functions. Thus was born the fundamental question of Fourier series. No less an eminence gris than Leonhard Euler argued against the proposition. Using the method of separation of variables, it was realized that the equation could be solved with a data function of the form?(x)= sin jx for j? Z.Itwasnaturaltoask, using the philosophy of superposition, whether the equation could then be solved with data on the interval [0,?] consisting of a nite linear combinationof the sin jx. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Codice articolo 9780817646684
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Explorations in Harmonic Analysis: With Applications to Complex Function Theory and the Heisenberg Group (Applied and Numerical Harmonic Analysis)
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Buch. Condizione: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -This self-contained text provides an introduction to modern harmonic analysis in the context in which it is actually applied, in particular, through complex function theory and partial differential equations. It takes the novice mathematical reader from the rudiments of harmonic analysis (Fourier series) to the Fourier transform, pseudodifferential operators, and finally to Heisenberg analysis. 362 pp. Englisch. Codice articolo 9780817646684
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Condizione: New. Print on Demand pp. 378 26 Illus. Codice articolo 7958929
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