Last edited by Tojale
Monday, May 11, 2020 | History

3 edition of Linear Theory of Colombeau Generalized Functions (Research Notes in Mathematics Series) found in the catalog.

Linear Theory of Colombeau Generalized Functions (Research Notes in Mathematics Series)

by M Nedeljkov

  • 155 Want to read
  • 26 Currently reading

Published by Chapman & Hall/CRC .
Written in English

    Subjects:
  • Functional analysis,
  • Mathematical modelling,
  • Mathematics for scientists & engineers,
  • Mathematics,
  • Mathematical Analysis,
  • Science/Mathematics,
  • Advanced,
  • Algebra - General,
  • Mathematics / Differential Equations,
  • Linear Programming

  • The Physical Object
    FormatHardcover
    Number of Pages168
    ID Numbers
    Open LibraryOL7880722M
    ISBN 100582356830
    ISBN 109780582356832

    In mathematics, generalized functions, or distributions, are objects extending the notion of functions. There is more than one recognized theory. There is more than one recognized theory. Generalized functions are especially useful in making discontinuous functions more like smooth functions, and describing discrete physical phenomena such as point charges. Global algebras of nonlinear generalized functions with applications in general relativity since (x) x= xj x=0 = 0 and xvp(1=x) = 1, where vp(1=x) denotes the Cauchy principal value of 1=x. A theory where = 0 would be point-less, since we explicitly want to model shocks and point charges. Similarly,Cited by: 3.

    1 Distributions or generalized functions. We start we the following synthesis of the introduction of the classical book by Gelfand-Shilov [GeSh64, page 1]. Physicist (and engineers?) have long been using ’singular functions’. The simples example is the delta function (x x 0).File Size: KB. We study integration and Fourier transform in the Colombeau algebra Gτ of tempered generalized functions using a general damping factor. This unifies Cited by:

    This book presents recent and very elementary developments of a theory of multiplication of distributions in the field of explicit and numerical solutions of systems of PDEs of physics (nonlinear elasticity, elastoplasticity, hydrodynamics, multifluid flows, acoustics). The abstract theory of generalized functions. Pages Colombeau. LINEAR RESPONSE THEORY This chapter is devoted to a concise presentation of linear response the-ory, which provides a general framework for analysing the dynamical properties of a condensed-matter system close to thermal equilibrium. The dynamical processes may either be spontaneous fluctuations, orFile Size: KB.


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Linear Theory of Colombeau Generalized Functions (Research Notes in Mathematics Series) by M Nedeljkov Download PDF EPUB FB2

Buy Linear Theory of Colombeau Generalized Functions (Chapman & Hall/CRC Research Notes in Mathematics Series) on FREE SHIPPING on qualified orders Linear Theory of Colombeau Generalized Functions (Chapman & Hall/CRC Research Notes in Mathematics Series): Nedeljkov, M, Pilipovic, S, Scarpalezos, D: : BooksAuthor: M Nedeljkov.

Linear Theory of Colombeau Generalized Functions - CRC Press Book Results from the now-classical distribution theory involving convolution and Fourier transformation are extended to cater for Colombeau's generalized functions.

Linear Theory of Colombeau Generalized Functions (Chapman & Hall/CRC Research Notes in Mathematics Series) (1st Edition) by S. Pilipovic, D. Nedeljkov Scarpalezos, Etc. Nedeljkov, M. Nedeljkovetc., Stevan Pilipović, D. Scarpalézos Paperback, Pages, Published Book Edition: 1st Edition.

Colombeau’s Theory of Generalized Functions. Abstract. The theory of distributions, founded by S. Sobolev and L. Schwartz, shows great power and flexibility in its natural domain, the theory of linear partial differential by: 2.

The author presents the notion of generalized functions, their properties and their applications for solving ordinary differential equations and partial differential equations. The author demonstrates through various examples that familiarity with generalized functions is very helpful for students in mathematics, Cited by: Abstract.

The class of Colombeau generalized functions has been introduced in the early eightees. A good pedagogical survey about this class and its related calculus can be found in [ 12 ].

Recently [ 13] has presented the state of the art on the actual theory and it has developed some numerical analysis by: Geometric Theory of Generalized Functions with Applications to General Relativity, M. Grosser, M. Kunzinger, M. Oberguggenberger, and R.

Steinbauer (). 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.

We describe a mathematical theory of nonlinear generalized functions based on Colombeau algebras and show how this may be applied in general relativity. We end by discussing the concept of singularity in general relativity and show that certain solutions with weak singularities may be regarded as distributional solutions of Einstein's by: Support of a The upports of a generalized unctionf f (x) is eth comlpemetn with respect to eth real line of het open set on iwhch f (x) = 0.

orF exalmpe, eth portsup of  (x) is the set f 0 g ; hatt is, the poitn x = 0. Appendix Fundamental Properties of Generalized Functions A.1 Definition of generalized functions First of all, let us give some material from mathematics, which is necessary for defining the concept of a generalized function.

Let us consider the following linear functional: T[ϕ(x)] = f(x)ϕ(x)dx. (A.1)File Size: KB. Book Description 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.

J.F. Colombeau’s non-linear theory of generalized functions is based on varieties of families of differential commutative rings G def= {G(Ω)}. Ω∈T such that: 1) Each G is a sheaf of differ- ential rings (consequently, each f ∈ G(Ω) has a support which is a closed set of Ω).

8 The Colombeau theory of generalized functions Deflnition A topological vector space X is called a Montel space if X is locally con- vex Hausdorfi such that every absorbing, covex, balanced and closed subset of X is a neighborhood of zero in File Size: KB.

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. Nonlinear Theory of Generalized Functions - CRC Press Book Questions regarding the interplay of nonlinearity and the creation and propagation of singularities arise in a variety of fields-including nonlinear partial differential equations, noise-driven stochastic partial differential equations, general relativity, and geometry with singularities.

Results from the classical distribution theory involving convolution and Fourier transformation are extended to cater for Colombeau's generalized functions in this text.

Indications are given how these particular generalized functions can be used. Purchase Elementary Introduction to New Generalized Functions, Volume - 1st Edition. Print Book & E-Book. ISBNBook Edition: 1. Colombeau algebra it becomes a generalized function (in short, a G-function) which can be manipulated in non-linear expressions as if it were an ordinary C ∞ Size: KB.

isomorphisms of algebras of colombeau generalized functions 3 W e will a lso use a slig htly modified version of the space G [ X, Y ] where we do not. Abstract. Let T stand for the usual topology on Rd. J.F.

Colombeau’s non-linear theory of generalized functions is based on varieties of families of differential commutative rings G def = {G(Ω)}Ω∈T such that: 1) Each G is a sheaf of differential rings (consequently, each f ∈ G(Ω) has a sup-port which is a closed set of Ω).

Linear and non-linear theory of generalized functions and its applications, – () Cached. Download Links [] {R. Steinbauer}, title = {A geometric approach to full Colombeau algebras. Linear and non-linear theory of generalized functions and its applications, –}, booktitle = {MR (g), Zbl MULTIPLICATION OF SCHWARTZ DISTRIBUTIONS AND COLOMBEAU GENERALIZED FUNCTIONS B.P.

DAMYANOV Received January 6, and, in revised form, Ap Abstract. The di erential C-algebra G(Rm) of generalized functions of J.-F. Colombeau contains the space D0(Rm)of Schwartz distributions.The Colombeau generalized function algebra is the factor algebra.

It contains the space of distributions with derivatives faithfully extended (cf. also Generalized function, derivative of a).

The asymptotic decay property expressed in together with an argument using Taylor expansion shows that is a faithful subalgebra.