On The Convergence Of Sum C Kf N Kx
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On the convergence of sum c kf n kx
Author | : Istvan Berkes,Michel Weber |
Publsiher | : American Mathematical Soc. |
Total Pages | : 88 |
Release | : 2009 |
Genre | : Convergence |
ISBN | : 9780821843246 |
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Presents a general study of the convergence problem and intends to prove several fresh results and improve a number of old results in the field. This title studies the case when the nk are random and investigates the discrepancy the sequence (nkx) mod 1.
Smooth Analysis in Banach Spaces
Author | : Petr Hájek,Michal Johanis |
Publsiher | : Walter de Gruyter GmbH & Co KG |
Total Pages | : 514 |
Release | : 2014-10-29 |
Genre | : Mathematics |
ISBN | : 9783110258998 |
Download Smooth Analysis in Banach Spaces Book in PDF, Epub and Kindle
This book is about the subject of higher smoothness in separable real Banach spaces. It brings together several angles of view on polynomials, both in finite and infinite setting. Also a rather thorough and systematic view of the more recent results, and the authors work is given. The book revolves around two main broad questions: What is the best smoothness of a given Banach space, and its structural consequences? How large is a supply of smooth functions in the sense of approximating continuous functions in the uniform topology, i.e. how does the Stone-Weierstrass theorem generalize into infinite dimension where measure and compactness are not available? The subject of infinite dimensional real higher smoothness is treated here for the first time in full detail, therefore this book may also serve as a reference book.
Introduction to Partial Differential Equations
Author | : Peter J. Olver |
Publsiher | : Springer Science & Business Media |
Total Pages | : 636 |
Release | : 2013-11-08 |
Genre | : Mathematics |
ISBN | : 9783319020990 |
Download Introduction to Partial Differential Equations Book in PDF, Epub and Kindle
This textbook is designed for a one year course covering the fundamentals of partial differential equations, geared towards advanced undergraduates and beginning graduate students in mathematics, science, engineering, and elsewhere. The exposition carefully balances solution techniques, mathematical rigor, and significant applications, all illustrated by numerous examples. Extensive exercise sets appear at the end of almost every subsection, and include straightforward computational problems to develop and reinforce new techniques and results, details on theoretical developments and proofs, challenging projects both computational and conceptual, and supplementary material that motivates the student to delve further into the subject. No previous experience with the subject of partial differential equations or Fourier theory is assumed, the main prerequisites being undergraduate calculus, both one- and multi-variable, ordinary differential equations, and basic linear algebra. While the classical topics of separation of variables, Fourier analysis, boundary value problems, Green's functions, and special functions continue to form the core of an introductory course, the inclusion of nonlinear equations, shock wave dynamics, symmetry and similarity, the Maximum Principle, financial models, dispersion and solutions, Huygens' Principle, quantum mechanical systems, and more make this text well attuned to recent developments and trends in this active field of contemporary research. Numerical approximation schemes are an important component of any introductory course, and the text covers the two most basic approaches: finite differences and finite elements.
An Easy Path to Convex Analysis and Applications
Author | : Boris Mordukhovich,Nguyen Mau |
Publsiher | : Springer Nature |
Total Pages | : 202 |
Release | : 2022-05-31 |
Genre | : Mathematics |
ISBN | : 9783031024061 |
Download An Easy Path to Convex Analysis and Applications Book in PDF, Epub and Kindle
Convex optimization has an increasing impact on many areas of mathematics, applied sciences, and practical applications. It is now being taught at many universities and being used by researchers of different fields. As convex analysis is the mathematical foundation for convex optimization, having deep knowledge of convex analysis helps students and researchers apply its tools more effectively. The main goal of this book is to provide an easy access to the most fundamental parts of convex analysis and its applications to optimization. Modern techniques of variational analysis are employed to clarify and simplify some basic proofs in convex analysis and build the theory of generalized differentiation for convex functions and sets in finite dimensions. We also present new applications of convex analysis to location problems in connection with many interesting geometric problems such as the Fermat-Torricelli problem, the Heron problem, the Sylvester problem, and their generalizations. Of course, we do not expect to touch every aspect of convex analysis, but the book consists of sufficient material for a first course on this subject. It can also serve as supplemental reading material for a course on convex optimization and applications.
The Journal of the Indian Mathematical Society
Author | : Indian Mathematical Society |
Publsiher | : Unknown |
Total Pages | : 912 |
Release | : 1959 |
Genre | : Mathematics |
ISBN | : UCAL:B3756252 |
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Vols. for 1923-32 include separately paged sections: "Notes and questions" and "Progress report."
Journal of the Optical Society of America
Author | : Anonim |
Publsiher | : Unknown |
Total Pages | : 712 |
Release | : 1998 |
Genre | : Imaging systems |
ISBN | : CHI:53153232 |
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Summability Calculus
Author | : Ibrahim M. Alabdulmohsin |
Publsiher | : Springer |
Total Pages | : 165 |
Release | : 2018-03-07 |
Genre | : Mathematics |
ISBN | : 9783319746487 |
Download Summability Calculus Book in PDF, Epub and Kindle
This book develops the foundations of "summability calculus", which is a comprehensive theory of fractional finite sums. It fills an important gap in the literature by unifying and extending disparate historical results. It also presents new material that has not been published before. Importantly, it shows how the study of fractional finite sums benefits from and contributes to many areas of mathematics, such as divergent series, numerical integration, approximation theory, asymptotic methods, special functions, series acceleration, Fourier analysis, the calculus of finite differences, and information theory. As such, it appeals to a wide audience of mathematicians whose interests include the study of special functions, summability theory, analytic number theory, series and sequences, approximation theory, asymptotic expansions, or numerical methods. Richly illustrated, it features chapter summaries, and includes numerous examples and exercises. The content is mostly developed from scratch using only undergraduate mathematics, such as calculus and linear algebra.