Gap And Density Theorems
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Gap And Density Theorems
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Author : Norman Levinson
language : en
Publisher: American Mathematical Soc.
Release Date : 1940-12-31
Gap And Density Theorems written by Norman Levinson and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1940-12-31 with Mathematics categories.
A typical gap theorem of the type discussed in the book deals with a set of exponential functions ${ \{e^{{{i\lambda}_n} x}\} }$ on an interval of the real line and explores the conditions under which this set generates the entire $L_2$ space on this interval. A typical gap theorem deals with functions $f$ on the real line such that many Fourier coefficients of $f$ vanish. The main goal of this book is to investigate relations between density and gap theorems and to study various cases where these theorems hold. The author also shows that density- and gap-type theorems are related to various properties of zeros of analytic functions in one variable.
Problems And Theorems In Analysis Ii
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Author : George Polya
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Problems And Theorems In Analysis Ii written by George Polya and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Few mathematical books are worth translating 50 years after original publication. Polyá-Szegö is one! It was published in German in 1924, and its English edition was widely acclaimed when it appeared in 1972. In the past, more of the leading mathematicians proposed and solved problems than today. Their collection of the best in analysis is a heritage of lasting value.
On Density Theorems In Real Rank 1
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Author : Mathematical Sciences Research Institute (Berkeley, Calif.).
language : en
Publisher:
Release Date : 1992
On Density Theorems In Real Rank 1 written by Mathematical Sciences Research Institute (Berkeley, Calif.). and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with categories.
Problems And Theorems In Analysis
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Author : Georg Polya
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Problems And Theorems In Analysis written by Georg Polya and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.
Fourier Techniques And Applications
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Author : John F. Price
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Fourier Techniques And Applications written by John F. Price and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The first systematic methods of Fourier analysis date from the early eighteenth century with the work of Joseph Fourier on the problem of the flow of heat. (A brief history is contained in the first paper.) Given the initial tempera ture at all points of a region, the problem was to determine the changes in the temperature distribution over time. Understanding and predicting these changes was important in such areas as the handling of metals and the determination of geological and atmospheric temperatures. Briefly, Fourier noticed that the solution of the heat diffusion problem was simple if the initial temperature dis tribution was sinusoidal. He then asserted that any distri bution can be decomposed into a sum of sinusoids, these being the harmonics of the original function. This meant that the general solution could now be obtained by summing the solu tions of the component sinusoidal problems. This remarkable ability of the series of sinusoids to describe all "reasonable" functions, the sine qua non of Fourier analysis and synthesis, has led to the routine use of the methods originating with Fourier in a great diversity of areas - astrophysics, computing, economics, electrical engineering, geophysics, information theory, medical engineering, optics, petroleum and mineral exploration, quan tum physics and spectroscopy, to name a few.
Advances In Shannon S Sampling Theory
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Author : AhmedI. Zayed
language : en
Publisher: Routledge
Release Date : 2018-04-24
Advances In Shannon S Sampling Theory written by AhmedI. Zayed and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-04-24 with Mathematics categories.
Advances in Shannon's Sampling Theory provides an up-to-date discussion of sampling theory, emphasizing the interaction between sampling theory and other branches of mathematical analysis, including the theory of boundary-value problems, frames, wavelets, multiresolution analysis, special functions, and functional analysis. The author not only traces the history and development of the theory, but also presents original research and results that have never before appeared in book form. Recent techniques covered include the Feichtinger-Gröchenig sampling theory; frames, wavelets, multiresolution analysis and sampling; boundary-value problems and sampling theorems; and special functions and sampling theorems. The book will interest graduate students and professionals in electrical engineering, communications, and applied mathematics.
Value Distribution Theory And Related Topics
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Author : Grigor A. Barsegian
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-05-02
Value Distribution Theory And Related Topics written by Grigor A. Barsegian and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-05-02 with Mathematics categories.
The Nevanlinna theory of value distribution of meromorphic functions, one of the milestones of complex analysis during the last century, was c- ated to extend the classical results concerning the distribution of of entire functions to the more general setting of meromorphic functions. Later on, a similar reasoning has been applied to algebroid functions, subharmonic functions and meromorphic functions on Riemann surfaces as well as to - alytic functions of several complex variables, holomorphic and meromorphic mappings and to the theory of minimal surfaces. Moreover, several appli- tions of the theory have been exploited, including complex differential and functional equations, complex dynamics and Diophantine equations. The main emphasis of this collection is to direct attention to a number of recently developed novel ideas and generalizations that relate to the - velopment of value distribution theory and its applications. In particular, we mean a recent theory that replaces the conventional consideration of counting within a disc by an analysis of their geometric locations. Another such example is presented by the generalizations of the second main theorem to higher dimensional cases by using the jet theory. Moreover, s- ilar ideas apparently may be applied to several related areas as well, such as to partial differential equations and to differential geometry. Indeed, most of these applications go back to the problem of analyzing zeros of certain complex or real functions, meaning in fact to investigate level sets or level surfaces.
Probabilistic And Stochastic Methods In Analysis With Applications
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Author : J.S. Byrnes
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Probabilistic And Stochastic Methods In Analysis With Applications written by J.S. Byrnes and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Probability has been an important part of mathematics for more than three centuries. Moreover, its importance has grown in recent decades, since the computing power now widely available has allowed probabilistic and stochastic techniques to attack problems such as speech and image processing, geophysical exploration, radar, sonar, etc. -- all of which are covered here. The book contains three exceptionally clear expositions on wavelets, frames and their applications. A further extremely active current research area, well covered here, is the relation between probability and partial differential equations, including probabilistic representations of solutions to elliptic and parabolic PDEs. New approaches, such as the PDE method for large deviation problems, and stochastic optimal control and filtering theory, are beginning to yield their secrets. Another topic dealt with is the application of probabilistic techniques to mathematical analysis. Finally, there are clear explanations of normal numbers and dynamic systems, and the influence of probability on our daily lives.
Nonuniform Sampling
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Author : Farokh Marvasti
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Nonuniform Sampling written by Farokh Marvasti and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Technology & Engineering categories.
Our understanding of nature is often through nonuniform observations in space or time. In space, one normally observes the important features of an object, such as edges. The less important features are interpolated. History is a collection of important events that are nonuniformly spaced in time. Historians infer between events (interpolation) and politicians and stock market analysts forecast the future from past and present events (extrapolation). The 20 chapters of Nonuniform Sampling: Theory and Practice contain contributions by leading researchers in nonuniform and Shannon sampling, zero crossing, and interpolation theory. Its practical applications include NMR, seismology, speech and image coding, modulation and coding, optimal content, array processing, and digital filter design. It has a tutorial outlook for practising engineers and advanced students in science, engineering, and mathematics. It is also a useful reference for scientists and engineers working in the areas of medical imaging, geophysics, astronomy, biomedical engineering, computer graphics, digital filter design, speech and video processing, and phased array radar.
Canadian Journal Of Mathematics
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Author :
language : en
Publisher:
Release Date : 1953
Canadian Journal Of Mathematics written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1953 with categories.