Author : B. S. Kashin
Publisher : American Mathematical Soc.
Page : 468 pages
File Size : 46,6 MB
Release : 2005-04-26
Category : Mathematics
ISBN : 9780821898239
Introductory concepts and some general results Independent functions and their first applications The Haar system Some results on the trigonometric and Walsh systems The Hilbert transform and some function spaces The Faber-Schauder and Franklin systems Orthogonalization and factorization theorems Theorems on the convergence of general orthogonal series General theorems on the divergence of orthogonal series Some theorems on the representation of functions by orthogonal series
Author : Greg Egan
Publisher : Gollancz
Page : 438 pages
File Size : 44,65 MB
Release : 2011-09-15
Category : Fiction
ISBN : 0575095156
In Yalda's universe, light has mass, no universal speed, and its creation generates energy; on Yalda's world, plants make food by emitting light into the dark night sky. And time is different: an astronaut might measure decades passing while visiting another star, only to return and find that just weeks have elapsed for her friends. On the farm where she lives, Yalda sees strange meteors that are entering the planetary system at an immense, unprecedented speed - and it soon becomes apparent that more of this ultra-fast material is appearing all the time, putting her world in terrible danger. An entire galaxy is about to collide with their own. There is one hope: a fleet sent straight towards the approaching galaxy, as fast as possible. Though it will feel like weeks back home, on board, millennia will pass before the collision, time enough to raise new generations, and time enough to find a way to stop the ultra-fast material. Either way, they have a chance to save everyone back on the home world.
Author : Harry F. Davis
Publisher : Courier Corporation
Page : 436 pages
File Size : 14,29 MB
Release : 2012-09-05
Category : Mathematics
ISBN : 0486140733
This incisive text deftly combines both theory and practical example to introduce and explore Fourier series and orthogonal functions and applications of the Fourier method to the solution of boundary-value problems. Directed to advanced undergraduate and graduate students in mathematics as well as in physics and engineering, the book requires no prior knowledge of partial differential equations or advanced vector analysis. Students familiar with partial derivatives, multiple integrals, vectors, and elementary differential equations will find the text both accessible and challenging. The first three chapters of the book address linear spaces, orthogonal functions, and the Fourier series. Chapter 4 introduces Legendre polynomials and Bessel functions, and Chapter 5 takes up heat and temperature. The concluding Chapter 6 explores waves and vibrations and harmonic analysis. Several topics not usually found in undergraduate texts are included, among them summability theory, generalized functions, and spherical harmonics. Throughout the text are 570 exercises devised to encourage students to review what has been read and to apply the theory to specific problems. Those preparing for further study in functional analysis, abstract harmonic analysis, and quantum mechanics will find this book especially valuable for the rigorous preparation it provides. Professional engineers, physicists, and mathematicians seeking to extend their mathematical horizons will find it an invaluable reference as well.
Author : A.S. Hedayat
Publisher : Springer Science & Business Media
Page : 433 pages
File Size : 39,21 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 1461214785
Orthogonal arrays have played a vital role in improving the quality of products manufactured throughout the world. This first book on the subject since its introduction more than fifty years ago serves as a key resource to this area of designing experiments. Most of the arrays obtained by the methods in this book are available electronically. Anyone running experiments - whether in a chemistry lab or a manufacturing plant, or in agricultural or medical research - will find this book useful.
Author : Sergeĭ Viktorovich Bochkarev
Publisher : American Mathematical Soc.
Page : 104 pages
File Size : 32,40 MB
Release : 1980
Category : Mathematics
ISBN : 9780821830451
"Investigate various forms of convergence of Fourier series in general orthonormal systems as well as certain problems in the theory of bases" -- Introduction.
Author : G. Alexits
Publisher : Elsevier
Page : 362 pages
File Size : 37,32 MB
Release : 2014-07-23
Category : Mathematics
ISBN : 1483222772
Convergence Problems of Orthogonal Series deals with the theory of convergence and summation of the general orthogonal series in relation to the general theory and classical expansions. The book reviews orthogonality, orthogonalization, series of orthogonal functions, complete orthogonal systems, and the Riesz-Fisher theorem. The text examines Jacobi polynomials, Haar's orthogonal system, and relations to the theory of probability using Rademacher's and Walsh's orthogonal systems. The book also investigates the convergence behavior of orthogonal series by methods belonging to the general theory of series. The text explains some Tauberian theorems and the classical Abel transform of the partial sums of a series which the investigator can use in the theory of orthogonal series. The book examines the importance of the Lebesgue functions for convergence problems, the generalization of the Walsh series, the order of magnitude of the Lebesgue functions, and the Lebesgue functions of the Cesaro summation. The text also deals with classical convergence problems in which general orthogonal series have limited significance as orthogonal expansions react upon the structural properties of the expanded function. This reaction happens under special assumptions concerning the orthogonal system in whose functions the expansion proceeds. The book can prove beneficial to mathematicians, students, or professor of calculus and advanced mathematics.
Author : Richard Askey
Publisher : SIAM
Page : 115 pages
File Size : 24,73 MB
Release : 1975-06-01
Category : Mathematics
ISBN : 0898710189
This volume presents the idea that one studies orthogonal polynomials and special functions to use them to solve problems.
Author : M Zuhair Nashed
Publisher : World Scientific
Page : 577 pages
File Size : 45,5 MB
Release : 2018-01-12
Category : Mathematics
ISBN : 981322889X
This volume aims to highlight trends and important directions of research in orthogonal polynomials, q-series, and related topics in number theory, combinatorics, approximation theory, mathematical physics, and computational and applied harmonic analysis. This collection is based on the invited lectures by well-known contributors from the International Conference on Orthogonal Polynomials and q-Series, that was held at the University of Central Florida in Orlando, on May 10-12, 2015. The conference was dedicated to Professor Mourad Ismail on his 70th birthday.The editors strived for a volume that would inspire young researchers and provide a wealth of information in an engaging format. Theoretical, combinatorial and computational/algorithmic aspects are considered, and each chapter contains many references on its topic, when appropriate.
Author : K B Datta
Publisher : World Scientific
Page : 289 pages
File Size : 20,88 MB
Release : 1995-05-31
Category : Mathematics
ISBN : 9814501581
This book provides a systematic and unified approach to the analysis, identification and optimal control of continuous-time dynamical systems via orthogonal polynomials such as Legendre, Laguerre, Hermite, Tchebycheff, Jacobi, Gegenbauer, and via orthogonal functions such as sine-cosine, block-pulse, and Walsh. This is the first book devoted to the application of orthogonal polynomials in systems and control, establishing the superiority of orthogonal polynomials to other orthogonal functions.
Author : Greg Egan
Publisher : Hachette UK
Page : 426 pages
File Size : 10,63 MB
Release : 2013-11-21
Category : Fiction
ISBN : 0575105798
In an alien universe where space and time play by different rules, interstellar voyages last longer for the travellers than for those they left behind. After six generations in flight, the inhabitants of the mountain-sized spacecraft the Peerless have used their borrowed time to develop advanced technology that could save their home world from annihilation. But not every traveller feels allegiance to a world they have never seen, and as tensions mount over the risks of turning the ship around and starting the long voyage home, a new complication arises: the prospect of constructing a messaging system that will give the Peerless news of its own future. While some of the crew welcome the opportunity to be warned of impending dangers - and perhaps even hear reports of the ship's triumphant return - others are convinced that knowing what lies ahead will be oppressive, and that the system will be abused. Agata longs for a chance to hear a message from the ancestors back on the home world, proving that the sacrifices of the travellers have not been in vain, but her most outspoken rival, Ramiro, fears that the system will undermine every decision the travellers make. When a vote fails to settle the matter and dissent erupts into violence, Ramiro, Agata and their allies must seek a new way to bring peace to the Peerless - by traveling to a world where time runs in reverse. THE ARROWS OF TIME is the final volume of the Orthogonal trilogy, bringing a powerful and surprising conclusion to the epic story of the Peerless that began with THE CLOCKWORK ROCKET and THE ETERNAL FLAME.
