Recent Applications of Harmonic Analysis to Function Spaces, Differential Equations, and Data Science (original) (raw)
Related papers
Trends in Harmonic Analysis and Its Applications
Contemporary Mathematics, 2015
It provides an in depth look at the many directions taken by experts in Harmonic Analysis and related areas. The papers cover topics such as frame theory, Gabor analysis, interpolation and Besov spaces on compact manifolds, Cuntz-Krieger algebras, reproducing kernel spaces, solenoids, hypergeometric shift operators and analysis on infinite dimensional groups. Expositions are by leading researchers in the field, both young and established. The papers consist of new results or new approaches to solutions, and at the same time provide an introduction into the respective subjects.
2015
It provides an in depth look at the many directions taken by experts in Harmonic Analysis and related areas. The papers cover topics such as frame theory, Gabor analysis, interpolation and Besov spaces on compact manifolds, Cuntz-Krieger algebras, reproducing kernel spaces, solenoids, hypergeometric shift operators and analysis on infinite dimensional groups. Expositions are by leading researchers in the field, both young and established. The papers consist of new results or new approaches to solutions, and at the same time provide an introduction into the respective subjects.
This paper discusses some of the numerical aspects of practical harmonic analysis. Topics include Historical Background, Fourier Series and Integral Approximations, Convergence Improvement, Differentiation of Fourier Series and Sigma Factors, Chebyshev Polynomial Approximations, The Tau Method, Fast Fourier Transforms, and Fast Sine or Cosine Transforms.
Advances in Harmonic Analysis and Operator Theory
2013
The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein.
Harmonic Analysis, Partial Differential Equations, Banach Spaces, and Operator Theory (Volume 2)
Association for Women in Mathematics series, 2017
Focusing on the groundbreaking work of women in mathematics past, present, and future, Springer's Association for Women in Mathematics Series presents the latest research and proceedings of conferences worldwide organized by the Association for Women in Mathematics (AWM). All works are peer-reviewed to meet the highest standards of scientific literature, while presenting topics at the cutting edge of pure and applied mathematics. Since its inception in 1971, The Association for Women in Mathematics has been a non-profit organization designed to help encourage women and girls to study and pursue active careers in mathematics and the mathematical sciences and to promote equal opportunity and equal treatment of women and girls in the mathematical sciences. Currently, the organization represents more than 3000 members and 200 institutions constituting a broad spectrum of the mathematical community, in the United States and around the world.
Graduate Texts in Mathematics, 2014
Institute of Mathematics of the Academy of Sciences of the Czech Republic provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use.
Harmonic Analysis and Partial Differential Equations
Contemporary Mathematics, 2010
We show that if a weight w ∈ C d 2t and there is q > 1 such that w 2t ∈ A d q , then the L 2-norm of the t-Haar multiplier of complexity (m, n) associated to w depends on the square root of the C d 2t-characteristic of w times the square root A d q-characteristic of w 2t times a constant that depends polynomially on the complexity. In particular, if w ∈ C d 2t ∩ A d ∞ then w 2t ∈ A d q for some q > 1.
Some new function spaces and their applications to Harmonic analysis
Journal of Functional Analysis, 1985
... SOME NEW FUNCTION SPACES 331 The proof proceeds by induction on k and a reduction via Theorem 5 from k to Al ... PROPOSITION 7. Suppose a is bounded; then u(x, t) = H,(aH,(a H,(a)) satisfies the condition (9.2) of Theorem 5. We start by observing that H,=(IP,)H, where H ...