Explorations in Harmonic Analysis

With Applications to Complex Function Theory and the Heisenberg Group
Buch | Hardcover
362 Seiten
2009
Birkhauser Boston Inc (Verlag)
978-0-8176-4668-4 (ISBN)

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Explorations in Harmonic Analysis - Steven G. Krantz
90,94 inkl. MwSt
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.

Ontology and History of Real Analysis.- The Central Idea: The Hilbert Transform.- Essentials of the Fourier Transform.- Fractional and Singular Integrals.- A Crash Course in Several Complex Variables.- Pseudoconvexity and Domains of Holomorphy.- Canonical Complex Integral Operators.- Hardy Spaces Old and New.- to the Heisenberg Group.- Analysis on the Heisenberg Group.- A Coda on Domains of Finite Type.

Erscheint lt. Verlag 5.5.2009
Reihe/Serie Applied and Numerical Harmonic Analysis
Zusatzinfo XIV, 362 p.
Verlagsort Secaucus
Sprache englisch
Maße 155 x 235 mm
Themenwelt Mathematik / Informatik Mathematik Analysis
ISBN-10 0-8176-4668-X / 081764668X
ISBN-13 978-0-8176-4668-4 / 9780817646684
Zustand Neuware
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