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Real and p-adic oscillatory integralsRogers, Keith McKenzie, School of Mathematics, UNSW January 2004 (has links)
After our introduction in Chapter 1, we consider van der Corput's lemma in Chapter 2. We find the nodes that minimize divided differences, and use these to find the sharp constant in a related sublevel set estimate. We go on to find the sharp constant in the first instance of the van der Corput lemma using a complex mean value theorem for integrals. With these bounds we improve the constant in the general van der Corput lemma, so that it is asymptotically sharp. In Chapter 3 we review the p-adic numbers and some results from Fourier analysis over the p-adics. In Chapter 4 we prove a p-adic version of van der Corput's lemma for polynomials, opening the way for the study of oscillatory integrals over the p-adics. In Chapter 5 we apply this result to bound maximal averages. We show that maximal averages over curves defined by p-adic polynomials are Lq bounded, where 1<q<infinity
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Singular integral operators associated to approximately homogeneous curvesWeinberg, David A. January 1980 (has links)
Thesis (Ph. D.)--University of Wisconsin--Madison, 1980. / Typescript. Vita. Description based on print version record. Includes bibliographical references (leaf 29).
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Wavelets and singular integral operators.January 1999 (has links)
by Lau Shui-kong, Francis. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1999. / Includes bibliographical references (leaves 95-98). / Abstracts in English and Chinese. / Chapter 1 --- General Theory of Wavelets --- p.8 / Chapter 1.1 --- Introduction --- p.8 / Chapter 1.2 --- Multiresolution Analysis and Wavelets --- p.9 / Chapter 1.3 --- Orthonormal Bases of Compactly Supported Wavelets --- p.12 / Chapter 1.3.1 --- Example : The Daubechies Wavelets --- p.15 / Chapter 1.4 --- Wavelets in Higher Dimensions --- p.20 / Chapter 1.4.1 --- Tensor product method --- p.20 / Chapter 1.4.2 --- Multiresolution Analysis in Rd --- p.21 / Chapter 1.5 --- Generalization to frames --- p.25 / Chapter 2 --- Wavelet Bases Numerical Algorithm --- p.27 / Chapter 2.1 --- The Algorithm in Wavelet Bases --- p.27 / Chapter 2.1.1 --- Definitions and Notations --- p.28 / Chapter 2.1.2 --- Fast Wavelet Transform --- p.31 / Chapter 2.2 --- Wavelet-Based Quadratures --- p.33 / Chapter 2.3 --- "The Integral Operator, Standard and Non-standard Form" --- p.39 / Chapter 2.3.1 --- The Standard Form --- p.40 / Chapter 2.3.2 --- The Non-standard Form --- p.41 / Chapter 2.4 --- The Calderon-Zygmund Operator and Numerical Cal- culation --- p.45 / Chapter 2.4.1 --- Numerical Algorithm to Construct the Non- standard Form --- p.45 / Chapter 2.4.2 --- Numerical Calculation and Compression of Op- erators --- p.45 / Chapter 2.5 --- Differential Operators in Wavelet Bases --- p.48 / Chapter 3 --- T(l)-Theorem of David and Journe --- p.55 / Chapter 3.1 --- Definitions and Notations --- p.55 / Chapter 3.1.1 --- T(l) Operator --- p.56 / Chapter 3.2 --- The Wavelet Proof of the T(l)-Theorem --- p.59 / Chapter 3.3 --- Proof of the T(l)-Theorem (Continue) --- p.64 / Chapter 3.4 --- Some recent results on the T(l)-Theorem --- p.70 / Chapter 4 --- Singular Values of Compact Pseudodifferential Op- erators --- p.72 / Chapter 4.1 --- Background --- p.73 / Chapter 4.1.1 --- Singular Values --- p.73 / Chapter 4.1.2 --- Schatten Class Ip --- p.73 / Chapter 4.1.3 --- The Ambiguity Function and the Wigner Dis- tribution --- p.74 / Chapter 4.1.4 --- Weyl Correspondence --- p.76 / Chapter 4.1.5 --- Gabor Frames --- p.78 / Chapter 4.2 --- Singular Values of Lσ --- p.82 / Chapter 4.3 --- The Calderon-Vaillancourt Theorem --- p.87 / Chapter 4.3.1 --- Holder-Zygmund Spaces --- p.87 / Chapter 4.3.2 --- Smooth Dyadic Resolution of Unity --- p.88 / Chapter 4.3.3 --- The proof of the Calderon-Vaillancourt The- orem --- p.89 / Bibliography
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Alguns resultados sobre a teoria de restrição da transformada de FourierAquino, Junielson Pantoja de January 2016 (has links)
A análise harmônica e o ramo da matemática que estuda a representação de funções ou sinais como a sobreposição de ondas base. Ela investiga e generaliza as noções das séries de Fourier e da transformação de Fourier. Neste trabalho, investigou-se um teorema de restrição da transformada de Fourier devido a Mitsis e Mockenhaupt (uma generalização do teorema de Stein-Tomas). Foram realizados estudos analíticos sobre o método para operadores integrais oscilatórios, baseado na fase estacionária. Os resultados permitem deduzir o teorema de restrição no plano (em seu caso geral) e o teorema de Carleson-Sjölin. / Harmonic analysis is the mathematical branch that studies the function or signals representation as a base wave overlay. It investigates and generalizes the notions of Fourier series and of the Fourier transform. In this work, was investigated a restriction theorem of the Fourier transform due to Mitsis and Mockenhaupt (a generalization of Stein-Tomas theorem) . Were performed analytic studies on the method for oscillating integral operators, based in the stationary phase. The results allow deducing the restriction theorem on the plane (in the general case) and the Carleson-Sjölin theorem.
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Singular integral operators on amalgam spaces. / CUHK electronic theses & dissertations collectionJanuary 2004 (has links)
by Hon-Ming Ho. / "May 2004." / Thesis (Ph.D.)--Chinese University of Hong Kong, 2004. / Includes bibliographical references (p. 69-71). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / Abstracts in English and Chinese.
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The Fredholm-Carlemann theory for a class of radically acting linear integral operators in H ( +) spaces /Keviczky, Attila Béla January 1976 (has links)
No description available.
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Zur Theorie der Dirichletschen Randwertaufgabe zum Operator ²-k⁴ im Innen- und Aussenraum mit der IntegralgleichungsmethodeWickel, Wolfram, January 1973 (has links)
Thesis--Bonn. / Vita. Includes bibliographical references (p. 74-75).
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Zur Theorie der Dirichletschen Randwertaufgabe zum Operator ²-k⁴ im Innen- und Aussenraum mit der IntegralgleichungsmethodeWickel, Wolfram, January 1973 (has links)
Thesis--Bonn. / Vita. Includes bibliographical references (p. 74-75).
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Der Neumannoperator in streng pseudokonvexen Gebieten mit gewichteter BergmanmetrikLampert, Christoph H. January 2003 (has links)
Thesis (doctoral)--Universität Bonn, 2003. / Includes bibliographical references (p. 163-165).
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Integralformeln und a priori-Abschätzungen für das [delta bar]-Neumann-ProblemStrauss, Albrecht. January 1988 (has links)
Thesis (doctoral)--Universität Bonn, 1988. / Cover title: Integraldarstellungen und a priori-Abschätzungen für das [delta bar]-Neumann-Problem. Includes bibliographical references (p. 94-96).
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