The Fundamental Principle for Systems of Convolution Equations PDF Download
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Author: Daniele Carlo Struppa
Publisher: American Mathematical Soc.
ISBN: 082182273X
Category : Convolutions
Languages : en
Pages : 175
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Book Description
The fundamental principle of L. Ehrenpreis states that under suitable hypotheses, the solutions of a homogeneous constant coefficients PDE can be represented as finite sums of absolutely convergent integrals over certain varieties in C[superscript italic]n. In the present paper the author extends these results to the case of homogeneous [italic]N x [script]m systems of convolution equations. In the first part of the paper, he discusses and extends an interpolation formula developed by Berenstein and Taylor, and uses the generalized Koszul complex to solve the algebraic problems which arise when considering systems in more than one unknown: the main result is a fundamental principle for general systems of convolution equations, in spaces [italic]X as described above. The second part of the paper is devoted to the generalization of this (and a related) result to more general classes of spaces, e.g. to the LAU-spaces of Ehrenpreis.
Author: Daniele Carlo Struppa
Publisher: American Mathematical Soc.
ISBN: 082182273X
Category : Convolutions
Languages : en
Pages : 175
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Book Description
The fundamental principle of L. Ehrenpreis states that under suitable hypotheses, the solutions of a homogeneous constant coefficients PDE can be represented as finite sums of absolutely convergent integrals over certain varieties in C[superscript italic]n. In the present paper the author extends these results to the case of homogeneous [italic]N x [script]m systems of convolution equations. In the first part of the paper, he discusses and extends an interpolation formula developed by Berenstein and Taylor, and uses the generalized Koszul complex to solve the algebraic problems which arise when considering systems in more than one unknown: the main result is a fundamental principle for general systems of convolution equations, in spaces [italic]X as described above. The second part of the paper is devoted to the generalization of this (and a related) result to more general classes of spaces, e.g. to the LAU-spaces of Ehrenpreis.
Author: Daniele Carlo Struppa
Publisher: American Mathematical Soc.
ISBN: 9780821822739
Category : Mathematics
Languages : en
Pages : 167
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Book Description
Author: Fabrizio Colombo
Publisher: Springer Science & Business Media
ISBN: 0817681663
Category : Mathematics
Languages : en
Pages : 344
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Book Description
* The main treatment is devoted to the analysis of systems of linear partial differential equations (PDEs) with constant coefficients, focusing attention on null solutions of Dirac systems * All the necessary classical material is initially presented * Geared toward graduate students and researchers in (hyper)complex analysis, Clifford analysis, systems of PDEs with constant coefficients, and mathematical physics
Author: Daniele Struppa
Publisher: American Mathematical Soc.
ISBN:
Category :
Languages : it
Pages : 167
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Book Description
Author:
Publisher:
ISBN:
Category : Functional analysis
Languages : en
Pages : 808
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Book Description
Author: C.A. Berenstein
Publisher: Birkhäuser
ISBN: 3034885601
Category : Mathematics
Languages : en
Pages : 169
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Book Description
A very primitive form of this monograph has existed for about two and a half years in the form of handwritten notes of a course that Alain Y ger gave at the University of Maryland. The objective, all along, has been to present a coherent picture of the almost mysterious role that analytic methods and, in particular, multidimensional residues, have recently played in obtaining effective estimates for problems in commutative algebra [71;5]* Our original interest in the subject rested on the fact that the study of many questions in harmonic analysis, like finding all distribution solutions (or finding out whether there are any) to a system of linear partial differential equa tions with constant coefficients (or, more generally, convolution equations) in ]R. n, can be translated into interpolation problems in spaces of entire functions with growth conditions. This idea, which one can trace back to Euler, is the basis of Ehrenpreis's Fundamental Principle for partial differential equations [37;5], [56;5], and has been explicitly stated, for convolution equations, in the work of Berenstein and Taylor [9;5] (we refer to the survey [8;5] for complete references. ) One important point in [9;5] was the use of the Jacobi interpo lation formula, but otherwise, the representation of solutions obtained in that paper were not explicit because of the use of a-methods to prove interpolation results.
Author: American Mathematical Society
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 576
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Book Description
Author: G.M. Khenkin
Publisher: Springer Science & Business Media
ISBN: 3642580114
Category : Mathematics
Languages : en
Pages : 292
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Book Description
This volume of the Encyclopaedia contains three contributions in the field of complex analysis; on mean periodicity and convolutionequations, Yang-Mills fields and the Radon-Penrose transform, and stringtheory. It is immensely useful to graduate students and researchers in complex analysis, differential geometry, quantum field theory, string theory and general relativity.
Author: Arun K. Tangirala
Publisher: CRC Press
ISBN: 143989602X
Category : Technology & Engineering
Languages : en
Pages : 908
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Book Description
Master Techniques and Successfully Build Models Using a Single Resource Vital to all data-driven or measurement-based process operations, system identification is an interface that is based on observational science, and centers on developing mathematical models from observed data. Principles of System Identification: Theory and Practice is an introductory-level book that presents the basic foundations and underlying methods relevant to system identification. The overall scope of the book focuses on system identification with an emphasis on practice, and concentrates most specifically on discrete-time linear system identification. Useful for Both Theory and Practice The book presents the foundational pillars of identification, namely, the theory of discrete-time LTI systems, the basics of signal processing, the theory of random processes, and estimation theory. It explains the core theoretical concepts of building (linear) dynamic models from experimental data, as well as the experimental and practical aspects of identification. The author offers glimpses of modern developments in this area, and provides numerical and simulation-based examples, case studies, end-of-chapter problems, and other ample references to code for illustration and training. Comprising 26 chapters, and ideal for coursework and self-study, this extensive text: Provides the essential concepts of identification Lays down the foundations of mathematical descriptions of systems, random processes, and estimation in the context of identification Discusses the theory pertaining to non-parametric and parametric models for deterministic-plus-stochastic LTI systems in detail Demonstrates the concepts and methods of identification on different case-studies Presents a gradual development of state-space identification and grey-box modeling Offers an overview of advanced topics of identification namely the linear time-varying (LTV), non-linear, and closed-loop identification Discusses a multivariable approach to identification using the iterative principal component analysis Embeds MATLAB® codes for illustrated examples in the text at the respective points Principles of System Identification: Theory and Practice presents a formal base in LTI deterministic and stochastic systems modeling and estimation theory; it is a one-stop reference for introductory to moderately advanced courses on system identification, as well as introductory courses on stochastic signal processing or time-series analysis.The MATLAB scripts and SIMULINK models used as examples and case studies in the book are also available on the author's website: http://arunkt.wix.com/homepage#!textbook/c397
Author: Chris Mack
Publisher: John Wiley & Sons
ISBN: 9780470723869
Category : Technology & Engineering
Languages : en
Pages : 534
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Book Description
The fabrication of an integrated circuit requires a variety of physical and chemical processes to be performed on a semiconductor substrate. In general, these processes fall into three categories: film deposition, patterning, and semiconductor doping. Films of both conductors and insulators are used to connect and isolate transistors and their components. By creating structures of these various components millions of transistors can be built and wired together to form the complex circuitry of modern microelectronic devices. Fundamental to all of these processes is lithography, ie, the formation of three-dimensional relief images on the substrate for subsequent transfer of the pattern to the substrate. This book presents a complete theoretical and practical treatment of the topic of lithography for both students and researchers. It comprises ten detailed chapters plus three appendices with problems provided at the end of each chapter. Additional Information: Visiting http://www.lithoguru.com/textbook/index.html enhances the reader's understanding as the website supplies information on how you can download a free laboratory manual, Optical Lithography Modelling with MATLAB®, to accompany the textbook. You can also contact the author and find help for instructors.
