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Showing 1 to 9 of 9 for “"Oscillatory integrals"”.
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Sharp estimates for trilinear oscillatory integral forms
… introduce some background of the trilinear oscillatory integrals and the motivations for their study. We also outline some key ideas in their proofs, as well as the major novelty of this dissertation. Chapter 2 serves as analytic preparation for the proof of our main theorem. We first extend …
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Lattice points in disks and strongly convex domains
… particular, we establish asymptotic results for oscillatory integrals and more specifically for Bessel functions. After examining the geometrical method for precisely counting the number of lattice points inside a disk of radius R, we use the Poisson Summation Formula and the Bessel function …
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A Riemann-Hilbert Approach to the Kissing Polynomials
Motivated by the numerical treatment of highly oscillatory integrals, this thesis studies a family of polynomials known as the Kissing Polynomials through Riemann-Hilbert techniques. The Kissing Polynomials are a family of non-Hermitian orthogonal polynomials, which are orthogonal with respect to …
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Numerical methods for systems of highly oscillatory ordinary differential equations
… contribution to the numerical analysis of highly oscillatory ordinary differential equations. Highly oscillatory functions appear to be at the forefront of the research in numerical analysis. In this work we developed efficient numerical algorithms for solving highly oscillatory differential …
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Asymptotic Expansion for the Time Evolution of the Probability Distribution Given by the Brownian Motion on Semialgebraic Sets
… for the occurrence of special parameterized integrals of a globally subanalytic function and the exponential function of a globally subanalytic function. This work is motivated by the work of Comte, Lion and Rolin, which considered parameterized integrals of globally subanalytic functions, of …
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Analytical and numerical techniques for wave scattering
… This requires the computation of singular highly-oscillatory integrals and we develop efficient numerical methods that can compute these integrals at frequency-independent cost. Finally, we provide a general result that allows the construction of recurrences for the efficient computation of …
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Dispersive estimates for the Schrödinger equation
Item withdrawn by Mark Zulauf (zulauf@illinois.edu) on 2010-06-30T12:54:50Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 1 Green_William.pdf: 999536 bytes, checksum: 87eb33f24c92fd62a4874b5db34bf8da (MD5)
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Analysis in Fractional Calculus and Asymptotics Related to Zeta Functions
… and modifications. Fractional derivatives and integrals are not uniquely defined: there are many different formulae, each of which has its own advantages and disadvantages. The most commonly used is the classical Riemann-Liouville model, but others may be preferred in different situations, and …