7 edition of **A nonlinear theory of generalized functions** found in the catalog.

- 251 Want to read
- 4 Currently reading

Published
**1990**
by Springer-Verlag in Berlin, New York
.

Written in English

- Theory of distributions (Functional analysis),
- Nonlinear theories.

**Edition Notes**

Includes bibliographical references (p. [201]-211) and index.

Statement | Hebe A. Biagioni. |

Series | Lecture notes in mathematics ;, 1421, Lecture notes in mathematics (Springer-Verlag) ;, 1421. |

Classifications | |
---|---|

LC Classifications | QA3 .L28 no. 1421, QA324 .L28 no. 1421 |

The Physical Object | |

Pagination | xii, 214 p. : |

Number of Pages | 214 |

ID Numbers | |

Open Library | OL1857372M |

ISBN 10 | 0387524088 |

LC Control Number | 90009578 |

Introduction to Non-Linear Algebra n and v ITEP, Moscow, Russia ABSTRACT Concise introduction to a relatively new subject of non-linear algebra: literal extension of text-book linear algebra to the case of non-linear equations and maps. This powerful science Cited by: This edited volume gives a new and integrated introduction to item response models (predominantly used in measurement applications in psychology, education, and other social science areas) from the viewpoint of the statistical theory of generalized linear and nonlinear mixed models. The new framework allows the domain of item response models to be co-ordinated and broadened to emphasize their.

Mathematics, an international, peer-reviewed Open Access journal. simple, reasonably general, nonlinear system theory could be developed. Hand in hand with this viewpoint was the feeling that many of the approaches useful for linear systems ought to be extensible to the nonlinear theory. This is a key point if the theory is .

Results from the now-classical distribution theory involving convolution and Fourier transformation are extended to cater for Colombeau's generalized functions. Indications are given how these particular generalized functions can be used to investigate linear equations and pseudo differential operators. Home Browse by Title Books Nonlinear approximation theory. Nonlinear approximation theory July July Power series equivalent to rational functions, Numerische Mathematik () A unified approach to methods for the simultaneous computation of all zeros of generalized polynomials, Numerische Mathematik, , (), Online.

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This book provides a simple introduction to a nonlinear theory of generalized functions introduced by J.F. Colombeau, which gives a meaning to any multiplication of by: About this book This book provides a simple introduction to a nonlinear theory of generalized functions introduced by J.F.

Colombeau, which gives a meaning to any multiplication of distributions. With a focus on applications, this books provides a compilation of recent approaches to the problem of singularities in nonlinear models.

The theory of differential algebras of generalized functions serves as the central theme of the project, along with its interrelations with classical : Paperback. With a focus on applications, this books provides a compilation of recent approaches to the problem of singularities in nonlinear models.

The theory of differential algebras of generalized functions serves as the central theme of the project, along with its interrelations with classical methods.

This book provides a simple introduction to a nonlinear theory of generalized functions introduced by J.F. Colombeau, which gives a meaning to any multiplication of distributions. This theory extends. A nonlinear theory of generalized functions.

[Hebe A Biagioni] -- This book provides a simple introduction to a nonlinear theory of generalized functions introduced by J.F. Colombeau, which gives a meaning to any multiplication of distributions.

The purpose of this article is to present an overview of a branch of nonlinear analysis that has taken up rapid development during the past decade: the theory of “multiplication of distributions” or better the “nonlinear theory of generalized functions”, as it goes far beyond the former topic by by: Over the past few years a certain shift of focus within the theory of algebras of generalized functions (in the sense of J.

Colombeau) has taken place. Originating in infinite dimensional analysis and initially applied mainly to problems in nonlinear partial differential equations involving. Part 2 examines the way Colombeau constructs a nonlinear theory of generalized functions and then succeeds in proving quite impressive existence, uniqueness, regularity, etc., results concerning generalized solutions of large classes of linear and nonlinear partial differential : This second edition of Generalized Functions has been strengthened in many ways.

The already extensive set of examples has been expanded. Since the publication of the first edition,there hasbeen tremendous growth inthe subject and Ihave attempted to incorporate some of these new concepts. Accordingly, almost all the chapters have been revised.

Fundamental Properties of Generalized Functions Fig. A.2 Real part of the ﬁrst element of the sequence {f 1/k(x)} (A) weakly converging to the delta function. Fig. A.3 Function f(x) (A) generating the fam-ily of scaled functions (A), which are weakly converging to the delta function File Size: KB.

Presented in two sections, part one describes Generalized Functions and Operator Theory, part two addresses Operator Theory and Dynamical Systems. The interplay between mathematics and physics is now more necessary than ever-and more difficult than ever, given the.

that “there will never exist a theory of generalized functions adapted to nonlinear calculations.” For the theory and applications of scalar valued nonlinear generalized func-tions, see the recent introductions in [3, 4, 15], the survey [5] and the book [10] on their use in continuum mechanics, and the survey [22] and the book [14] onCited by: 3.

CHAPTER 8. NONLINEAR LEAST SQUARES THEORY to allow for smoother transitions of structures. It is typical to choose the function h as a distribution function, e.g., h(y t−d;c,δ)= 1 1+exp[−(y t−d −c)/δ], wherec is still the threshold value and δ is a scale parameter.

This leads to the following smooth threshold autoregressive (STAR File Size: KB. Download Distribution Theory (Generalized Functions) Notes Download free online book chm pdf. The aim of this note is to give an introduction to nonlinear Fourier analysis from a harmonic analyst’s point of view.

This book focuses on the material analysis based on Fourier transform theory. The book chapters are related to FTIR and the. Download Distribution Theory (Generalized Functions) Notes Download free online book chm pdf. / Mathematics Books / Mathematical-Analysis Books / Fourier Analysis Books / Distribution Theory (Generalized Functions) Notes.

The aim of this note is to give an introduction to nonlinear Fourier analysis from a harmonic analyst’s point of. An introduction to a nonlinear theory of generalized functions introduced by J F Colombeau, which gives a meaning to any multiplication of distributions.

It is suitable for. It has been widely believed for half a century that there will never exist a nonlinear theory of generalized functions, in any mathematical context.

The aim of this text is to show the converse is. Linear, Nonlinear, Ordinary, Partial to the theory of generalized functions.

The advantage of this approach is that a The second part of the book is concerned with nonlinear problems and more advanced techniques.

Although we have used a lot of the material in Chapters 9. An axiomatic approach to the nonlinear theory of generalized functions and consistency of Laplace transforms Todor D.

Todorov Mathematics Department, California Polytechnic State University, San Luis Obispo, CA,USA Correspondence [email protected]

However in [J.F. Colombeau, M. Langlais, Generalized solutions of nonlinear parabolic equations with distributions as initial conditions, J.

Math. Anal. Appl () –] Colombeau and Langlais prove that these equations have a unique solution even if the δ -measure is substituted by any Colombeau generalized function of compact by: Colombeau's nonlinear theory of generalized functions ([7,8]) is based on viewing generalized functions as equivalence classes of smooth maps, encoding degrees of singularity in terms of asymptotic.CHAPTER 2 GENERALIZED SOLUTIONS OF NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS PRELIMINARY REMARKS Suppose given an m-th order nonltnear partial differential equa t ion () T(D)U(x) = 0, x E n C Rn wave equation in as for instance the first () or () () U t + U x * U = 0.

order shock (t.~) E (O.m)xR1 It is parttcularly tmportant to note that, when we .