# Browsing by Subject "Harmonic analysis"

Now showing 1 - 8 of 8

###### Results Per Page

###### Sort Options

Item Applications of special function theory to complex analysis(Texas Tech University, 2002-05) Cole, Leah JoanneShow more Not availableShow more Item Cesaro summability of Fourier series in LP-spaces(Texas Tech University, 1965-05) Amburgey, Jay KayShow more Not availableShow more Item Combinatorial and probabilistic techniques in harmonic analysis(2012-05) Lewko, Mark J., 1983-; Vaaler, Jeffrey D.; Beckner, William; Pavlovic, Natasa; Rodriguez-Villegas, Fernando; Zuckerman, DavidShow more We prove several theorems in the intersection of harmonic analysis, combinatorics, probability and number theory. In the second section we use combinatorial methods to construct various sets with pathological combinatorial properties. In particular, we answer a question of P. Erdos and V. Sos regarding unions of Sidon sets. In the third section we use incidence bounds and bilinear methods to prove several new endpoint restriction estimates for the Paraboloid over finite fields. In the fourth and fifth sections we study a variational maximal operators associated to orthonormal systems. Here we use probabilistic techniques to construct well-behaved rearrangements and base changes. In the sixth section we apply our variational estimates to a problem in sieve theory. In the seventh section, motivated by applications to sieve theory, we disprove a maximal inequality related to multiplicative characters.Show more Item Extremality, symmetry and regularity issues in harmonic analysis(2009-05) Carneiro, Emanuel Augusto de Souza; Beckner, WilliamShow more In this Ph. D. thesis we discuss four different problems in analysis: (a) sharp inequalities related to the restriction phenomena for the Fourier transform, with emphasis on some Strichartz-type estimates; (b) extremal approximations of exponential type for the Gaussian and for a class of even functions, with applications to analytic number theory; (c) radial symmetrization approach to convolution-like inequalities for the Boltzmann collision operator; (d) regularity of maximal operators with respect to weak derivatives and weak continuity.Show more Item Flexible fitting in 3D EM(2012-12) Bettadapura Raghu, Prasad Radhakrishna; Bajaj, Chandrajit; Crawford, Richard; Chen, Dongmei; Truskett, Thomas; Ying, LexingShow more In flexible fitting, the high-resolution crystal structure of a molecule is deformed to optimize its position with respect to a low-resolution density map. Solving the flexible fitting problem entails answering the following questions: (A) How can the crystal structure be deformed? (B) How can the term "optimum" be defined? and (C) How can the optimization problem be solved? In this dissertation, we answer the above questions in reverse order. (C) We develop PFCorr, a non-uniform SO(3)-Fourier-based tool to efficiently conduct rigid-body correlations over arbitrary subsets of the space of rigid-body motions. (B) We develop PF2Fit, a rigid-body fitting tool that provides several useful definitions of the optimal fit between the crystal structure and the density map while using PFCorr to search over the space of rigid-body motions (A) We develop PF3Fit, a flexible fitting tool that deforms the crystal structure with a hierarchical domain-based flexibility model while using PF2Fit to optimize the fit with the density map. Our contributions help us solve the rigid-body and flexible fitting problems in unique and advantageous ways. They also allow us to develop a generalized framework that extends, breadth-wise, to other problems in computational structural biology, including rigid-body and flexible docking, and depth-wise, to the question of interpreting the motions inherent to the crystal structure. Publicly-available implementations of each of the above tools additionally provide a window into the technically diverse fields of applied mathematics, structural biology, and 3D image processing, fields that we attempt, in this dissertation, to span.Show more Item Marcel Grandjany's harp transcriptions and editions(Texas Tech University, 2004-08) Parsons, Jeffrey LeeShow more Marcel Grandjany (1891-1975) is well known as an outstanding harpist, teacher and composer for the harp, Beyond this, however, he is also very important for his transcriptions for the harp of music originally written for other instruments, and also for bis editions of older works for the harp that had fallen into obscurity, Many of these transcriptions form a basic core of the modem harpist's repertoire, particularly of pre- Classical works. In addition, his transcriptions have generally been regarded as particularly idiomatic for the harp, utilizing the modem instrument's full range and an array of techniques common in the twentieth century, This dissertation examines ten representative Grandjany transcriptions, to pinpoint what changes Grandjany made, and what purpose these changes serve in adapting the original work for the harp, Such an understanding could be very useful for harpist or other musicians either transcribing or composing for the harp, Grandjany was, however, a man of his own time, and his transcriptions reflect a Romantic sensibility that is often at odds with the modem understanding of historically informed performance, This study attempts to identify non-stylistic elements added by Grandjany, and to determine what the modem performer might do to retain Grandjany's idiomatic sense without losing historical accuracy.Show more Item Methods of dynamical systems, harmonic analysis and wavelets applied to several physical systems(2002) Petrov, Nikola Petrov; Llave, Rafael de laShow more Item Observability and the inverse problem in electrocardiography(Texas Tech University, 1990-12) Iakovidis, IliasShow more The problem of observability of a system governed by a partial differential equation is considered. This problem arises in electrocardiography, and the goal is to reconstruct the electrical potentials on the surface of the heart from the information obtained noninvasively on the torso surface. The formulation of the problem leads to a Cauchy problem for the Laplace's equation, i.e., a harmonic function is sought in some region, given that the values of the function and its normal derivative are specified only on some part of the boundary. The aim of this dissertation is to investigate the feasibility of recovering the solution, given only discrete boundary measurements. First, the existence and the uniqueness of the solution are shown based on some general assumptions about the geometry and the function representing the electrical potentials of the surface of the heart. Then, a spherical model representing the heart-torso model is introduced and an analytical solution to the problem is obtained. Then, a regularization method is developed and some error estimates of the solution are obtained based on some a priori assumptions about the solution. Finally, the approximation on the surface of a sphere, by means of a numerical integration is considered, and the dependence of the solution on the location and the number of measurements is investigated.Show more