Download or read book Singular Integrals and Rectifiable Sets in Rn written by Guy David and published by . This book was released on 1991 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Rectifiability written by Pertti Mattila and published by Cambridge University Press. This book was released on 2023-01-12 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt: Rectifiable sets, measures, currents and varifolds are foundational concepts in geometric measure theory. The last four decades have seen the emergence of a wealth of connections between rectifiability and other areas of analysis and geometry, including deep links with the calculus of variations and complex and harmonic analysis. This short book provides an easily digestible overview of this wide and active field, including discussions of historical background, the basic theory in Euclidean and non-Euclidean settings, and the appearance of rectifiability in analysis and geometry. The author avoids complicated technical arguments and long proofs, instead giving the reader a flavour of each of the topics in turn while providing full references to the wider literature in an extensive bibliography. It is a perfect introduction to the area for researchers and graduate students, who will find much inspiration for their own research inside.
Download or read book Singular Integral Operators Quantitative Flatness and Boundary Problems written by Juan José Marín and published by Springer Nature. This book was released on 2022-09-29 with total page 605 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides a state-of-the-art, self-contained account on the effectiveness of the method of boundary layer potentials in the study of elliptic boundary value problems with boundary data in a multitude of function spaces. Many significant new results are explored in detail, with complete proofs, emphasizing and elaborating on the link between the geometric measure-theoretic features of an underlying surface and the functional analytic properties of singular integral operators defined on it. Graduate students, researchers, and professionals interested in a modern account of the topic of singular integral operators and boundary value problems – as well as those more generally interested in harmonic analysis, PDEs, and geometric analysis – will find this text to be a valuable addition to the mathematical literature.
Download or read book Discrete Energy on Rectifiable Sets written by Sergiy V. Borodachov and published by Springer Nature. This book was released on 2019-10-31 with total page 666 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book aims to provide an introduction to the broad and dynamic subject of discrete energy problems and point configurations. Written by leading authorities on the topic, this treatise is designed with the graduate student and further explorers in mind. The presentation includes a chapter of preliminaries and an extensive Appendix that augments a course in Real Analysis and makes the text self-contained. Along with numerous attractive full-color images, the exposition conveys the beauty of the subject and its connection to several branches of mathematics, computational methods, and physical/biological applications. This work is destined to be a valuable research resource for such topics as packing and covering problems, generalizations of the famous Thomson Problem, and classical potential theory in Rd. It features three chapters dealing with point distributions on the sphere, including an extensive treatment of Delsarte–Yudin–Levenshtein linear programming methods for lower bounding energy, a thorough treatment of Cohn–Kumar universality, and a comparison of 'popular methods' for uniformly distributing points on the two-dimensional sphere. Some unique features of the work are its treatment of Gauss-type kernels for periodic energy problems, its asymptotic analysis of minimizing point configurations for non-integrable Riesz potentials (the so-called Poppy-seed bagel theorems), its applications to the generation of non-structured grids of prescribed densities, and its closing chapter on optimal discrete measures for Chebyshev (polarization) problems.
Download or read book Reifenberg Parameterizations for Sets with Holes written by Guy David and published by American Mathematical Soc.. This book was released on 2012 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors extend the proof of Reifenberg's Topological Disk Theorem to allow the case of sets with holes, and give sufficient conditions on a set $E$ for the existence of a bi-Lipschitz parameterization of $E$ by a $d$-dimensional plane or smooth manifold. Such a condition is expressed in terms of square summability for the P. Jones numbers $\beta_1(x,r)$. In particular, it applies in the locally Ahlfors-regular case to provide very big pieces of bi-Lipschitz images of $\mathbb R^d$.
Download or read book Rectifiable Measures Square Functions Involving Densities and the Cauchy Transform written by Xavier Tolsa and published by American Mathematical Soc.. This book was released on 2017-01-18 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is devoted to the proof of two related results. The first one asserts that if is a Radon measure in satisfyingfor -a.e. , then is rectifiable. Since the converse implication is already known to hold, this yields the following characterization of rectifiable sets: a set with finite -dimensional Hausdorff measure is rectifiable if and only ifH^1x2EThe second result of the monograph deals with the relationship between the above square function in the complex plane and the Cauchy transform . Assuming that has linear growth, it is proved that is bounded in if and only iffor every square .
Download or read book From Operator Theory to Orthogonal Polynomials Combinatorics and Number Theory written by Fritz Gesztesy and published by Springer Nature. This book was released on 2021-11-11 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main topics of this volume, dedicated to Lance Littlejohn, are operator and spectral theory, orthogonal polynomials, combinatorics, number theory, and the various interplays of these subjects. Although the event, originally scheduled as the Baylor Analysis Fest, had to be postponed due to the pandemic, scholars from around the globe have contributed research in a broad range of mathematical fields. The collection will be of interest to both graduate students and professional mathematicians. Contributors are: G.E. Andrews, B.M. Brown, D. Damanik, M.L. Dawsey, W.D. Evans, J. Fillman, D. Frymark, A.G. García, L.G. Garza, F. Gesztesy, D. Gómez-Ullate, Y. Grandati, F.A. Grünbaum, S. Guo, M. Hunziker, A. Iserles, T.F. Jones, K. Kirsten, Y. Lee, C. Liaw, F. Marcellán, C. Markett, A. Martinez-Finkelshtein, D. McCarthy, R. Milson, D. Mitrea, I. Mitrea, M. Mitrea, G. Novello, D. Ong, K. Ono, J.L. Padgett, M.M.M. Pang, T. Poe, A. Sri Ranga, K. Schiefermayr, Q. Sheng, B. Simanek, J. Stanfill, L. Velázquez, M. Webb, J. Wilkening, I.G. Wood, M. Zinchenko.
Download or read book Singular Integrals and Rectifiability written by Daniel Girela Sarrión and published by . This book was released on 2016 with total page 107 pages. Available in PDF, EPUB and Kindle. Book excerpt: Vegeu resums dgs1de1.pdf.
Download or read book Analytic Capacity Rectifiability Menger Curvature and Cauchy Integral written by Hervé Pajot and published by Springer Science & Business Media. This book was released on 2002-11-26 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on a graduate course given by the author at Yale University this book deals with complex analysis (analytic capacity), geometric measure theory (rectifiable and uniformly rectifiable sets) and harmonic analysis (boundedness of singular integral operators on Ahlfors-regular sets). In particular, these notes contain a description of Peter Jones' geometric traveling salesman theorem, the proof of the equivalence between uniform rectifiability and boundedness of the Cauchy operator on Ahlfors-regular sets, the complete proofs of the Denjoy conjecture and the Vitushkin conjecture (for the latter, only the Ahlfors-regular case) and a discussion of X. Tolsa's solution of the Painlevé problem.
Download or read book Singular Integrals and Related Topics written by Shanzhen Lu and published by World Scientific. This book was released on 2007 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces some important progress in the theory of CalderonOCoZygmund singular integrals, oscillatory singular integrals, and LittlewoodOCoPaley theory over the last decade. It includes some important research results by the authors and their cooperators, such as singular integrals with rough kernels on Block spaces and Hardy spaces, the criterion on boundedness of oscillatory singular integrals, and boundedness of the rough Marcinkiewicz integrals. These results have frequently been cited in many published papers."
Download or read book Harmonic Analysis and Applications written by Carlos E. Kenig and published by American Mathematical Soc.. This book was released on 2020-12-14 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: The origins of the harmonic analysis go back to an ingenious idea of Fourier that any reasonable function can be represented as an infinite linear combination of sines and cosines. Today's harmonic analysis incorporates the elements of geometric measure theory, number theory, probability, and has countless applications from data analysis to image recognition and from the study of sound and vibrations to the cutting edge of contemporary physics. The present volume is based on lectures presented at the summer school on Harmonic Analysis. These notes give fresh, concise, and high-level introductions to recent developments in the field, often with new arguments not found elsewhere. The volume will be of use both to graduate students seeking to enter the field and to senior researchers wishing to keep up with current developments.
Download or read book Singular Integrals and Differentiability Properties of Functions PMS 30 Volume 30 written by Elias M. Stein and published by Princeton University Press. This book was released on 2016-06-02 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: Singular integrals are among the most interesting and important objects of study in analysis, one of the three main branches of mathematics. They deal with real and complex numbers and their functions. In this book, Princeton professor Elias Stein, a leading mathematical innovator as well as a gifted expositor, produced what has been called the most influential mathematics text in the last thirty-five years. One reason for its success as a text is its almost legendary presentation: Stein takes arcane material, previously understood only by specialists, and makes it accessible even to beginning graduate students. Readers have reflected that when you read this book, not only do you see that the greats of the past have done exciting work, but you also feel inspired that you can master the subject and contribute to it yourself. Singular integrals were known to only a few specialists when Stein's book was first published. Over time, however, the book has inspired a whole generation of researchers to apply its methods to a broad range of problems in many disciplines, including engineering, biology, and finance. Stein has received numerous awards for his research, including the Wolf Prize of Israel, the Steele Prize, and the National Medal of Science. He has published eight books with Princeton, including Real Analysis in 2005.
Download or read book Singular Integrals and Rectifiability of Measures in the Plane written by Petri Huovinen and published by . This book was released on 1997 with total page 63 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Trends in Harmonic Analysis written by Massimo A. Picardello and published by Springer Science & Business Media. This book was released on 2012-12-05 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book illustrates the wide range of research subjects developed by the Italian research group in harmonic analysis, originally started by Alessandro Figà-Talamanca, to whom it is dedicated in the occasion of his retirement. In particular, it outlines some of the impressive ramifications of the mathematical developments that began when Figà-Talamanca brought the study of harmonic analysis to Italy; the research group that he nurtured has now expanded to cover many areas. Therefore the book is addressed not only to experts in harmonic analysis, summability of Fourier series and singular integrals, but also in potential theory, symmetric spaces, analysis and partial differential equations on Riemannian manifolds, analysis on graphs, trees, buildings and discrete groups, Lie groups and Lie algebras, and even in far-reaching applications as for instance cellular automata and signal processing (low-discrepancy sampling, Gaussian noise).
Download or read book Geometric Harmonic Analysis IV written by Dorina Mitrea and published by Springer Nature. This book was released on 2023-07-09 with total page 1004 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents a comprehensive, self-contained, and novel approach to the Divergence Theorem through five progressive volumes. Its ultimate aim is to develop tools in Real and Harmonic Analysis, of geometric measure theoretic flavor, capable of treating a broad spectrum of boundary value problems formulated in rather general geometric and analytic settings. The text is intended for researchers, graduate students, and industry professionals interested in applications of harmonic analysis and geometric measure theory to complex analysis, scattering, and partial differential equations. Traditionally, the label “Calderón-Zygmund theory” has been applied to a distinguished body of works primarily pertaining to the mapping properties of singular integral operators on Lebesgue spaces, in various geometric settings. Volume IV amounts to a versatile Calderón-Zygmund theory for singular integral operators of layer potential type in open sets with uniformly rectifiable boundaries, considered on a diverse range of function spaces. Novel applications to complex analysis in several variables are also explored here.
Download or read book Harmonic Measure written by John B. Garnett and published by Cambridge University Press. This book was released on 2005-04-04 with total page 4 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the last two decades several remarkable new results were discovered about harmonic measure in the complex plane. This book provides a careful survey of these results and an introduction to the branch of analysis which contains them. Many of these results, due to Bishop, Carleson, Jones, Makarov, Wolff and others, appear here in paperback for the first time. The book is accessible to students who have completed standard graduate courses in real and complex analysis. The first four chapters provide the needed background material on univalent functions, potential theory, and extremal length, and each chapter has many exercises to further inform and teach the readers.
Download or read book L p Square Function Estimates on Spaces of Homogeneous Type and on Uniformly Rectifiable Sets written by Steve Hofmann and published by American Mathematical Soc.. This book was released on 2017-01-18 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors establish square function estimates for integral operators on uniformly rectifiable sets by proving a local theorem and applying it to show that such estimates are stable under the so-called big pieces functor. More generally, they consider integral operators associated with Ahlfors-David regular sets of arbitrary codimension in ambient quasi-metric spaces. The local theorem is then used to establish an inductive scheme in which square function estimates on so-called big pieces of an Ahlfors-David regular set are proved to be sufficient for square function estimates to hold on the entire set. Extrapolation results for and Hardy space versions of these estimates are also established. Moreover, the authors prove square function estimates for integral operators associated with variable coefficient kernels, including the Schwartz kernels of pseudodifferential operators acting between vector bundles on subdomains with uniformly rectifiable boundaries on manifolds.
