scholarly journals Distinguished Elements in a Space of Distributions

1960 ◽  
Vol 24 (3) ◽  
pp. 527-533 ◽  
Author(s):  
Ken-ichi Miyazaki
Keyword(s):  
Space Of Distributions

scholarly journals Translation and modulation invariant Hilbert spaces

2021 ◽  
Author(s):  
Joachim Toft ◽  
Anupam Gumber ◽  
Ramesh Manna ◽  
P. K. Ratnakumar
Keyword(s):  
Hilbert Space ◽  
Hilbert Spaces ◽  
Zero Element ◽  
Multiplicative Constant ◽  
Space Of Distributions ◽  
Feichtinger Algebra

AbstractLet $$\mathcal H$$ H be a Hilbert space of distributions on $$\mathbf{R}^{d}$$ R d which contains at least one non-zero element of the Feichtinger algebra $$S_0$$ S 0 and is continuously embedded in $$\mathscr {D}'$$ D ′ . If $$\mathcal H$$ H is translation and modulation invariant, also in the sense of its norm, then we prove that $$\mathcal H= L^2$$ H = L 2 , with the same norm apart from a multiplicative constant.

scholarly journals Codimension One Holomorphic Distributions on the Projective Three-space

2018 ◽  
Vol 2020 (23) ◽  
pp. 9011-9074 ◽  
Author(s):  
Omegar Calvo-Andrade ◽  
Maurício Corrêa ◽  
Marcos Jardim
Keyword(s):  
Projective Space ◽  
Moduli Space ◽  
Tangent Bundle ◽  
Projective Variety ◽  
Arbitrary Degree ◽  
Codimension One ◽  
Quot Scheme ◽  
Space Of Distributions ◽  
Three Space

Abstract We study codimension one holomorphic distributions on the projective three-space, analyzing the properties of their singular schemes and tangent sheaves. In particular, we provide a classification of codimension one distributions of degree at most 2 with locally free tangent sheaves and show that codimension one distributions of arbitrary degree with only isolated singularities have stable tangent sheaves. Furthermore, we describe the moduli space of distributions in terms of Grothendieck’s Quot-scheme for the tangent bundle. In certain cases, we show that the moduli space of codimension one distributions on the projective space is an irreducible, nonsingular quasi-projective variety. Finally, we prove that every rational foliation and certain logarithmic foliations have stable tangent sheaves.

scholarly journals An embedding of Schwartz distributions in the algebra of asymptotic functions

1998 ◽  
Vol 21 (3) ◽  
pp. 417-428 ◽  
Author(s):  
Michael Oberguggenberger ◽  
Todor Todorov
Keyword(s):  
Differential Algebra ◽  
Generalized Functions ◽  
Schwartz Distributions ◽  
Asymptotic Functions ◽  
Space Of Distributions ◽  
Asymptotic Function

We present a solution of the problem of multiplication of Schwartz distributions by embedding the space of distributions into a differential algebra of generalized functions, called in the paper “asymptotic function,” similar to but different from J. F Colombeau's algebras of new generalized functions.

scholarly journals On two new characterizations of Steiltjes transforms for distributions

1985 ◽  
Vol 8 (4) ◽  
pp. 719-723
Author(s):  
Sunil Kumar Sinha
Keyword(s):  
Stieltjes Transform ◽  
Space Of Distributions ◽  
Definition Of

Two new characterizations of the Stieltjes transform for distribution are developed, using two transformations on the space of distributions viz., dilationUnand exponential shiftsT−p. The standard theorem on analyticity, uniqueness and invertibility of the Stieltjes transform are proved, using the new characterization as the definition of the Stieltjes transform.

scholarly journals Some Properties of Univariate and Multivariate Exponential Power Distributions and Related Topics

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1918
Author(s):  
Victor Korolev
Keyword(s):  
Limit Theorems ◽  
Random Sums ◽  
Random Vectors ◽  
Asymptotic Results ◽  
Space Of Distributions ◽  
Gamma Distributions ◽  
Statistical Regularities ◽  
Exponential Power ◽  
The One ◽  
Multivariate Exponential

In the paper, a survey of the main results concerning univariate and multivariate exponential power (EP) distributions is given, with main attention paid to mixture representations of these laws. The properties of mixing distributions are considered and some asymptotic results based on mixture representations for EP and related distributions are proved. Unlike the conventional analytical approach, here the presentation follows the lines of a kind of arithmetical approach in the space of random variables or vectors. Here the operation of scale mixing in the space of distributions is replaced with the operation of multiplication in the space of random vectors/variables under the assumption that the multipliers are independent. By doing so, the reasoning becomes much simpler, the proofs become shorter and some general features of the distributions under consideration become more vivid. The first part of the paper concerns the univariate case. Some known results are discussed and simple alternative proofs for some of them are presented as well as several new results concerning both EP distributions and some related topics including an extension of Gleser’s theorem on representability of the gamma distribution as a mixture of exponential laws and limit theorems on convergence of the distributions of maximum and minimum random sums to one-sided EP distributions and convergence of the distributions of extreme order statistics in samples with random sizes to the one-sided EP and gamma distributions. The results obtained here open the way to deal with natural multivariate analogs of EP distributions. In the second part of the paper, we discuss the conventionally defined multivariate EP distributions and introduce the notion of projective EP (PEP) distributions. The properties of multivariate EP and PEP distributions are considered as well as limit theorems establishing the conditions for the convergence of multivariate statistics constructed from samples with random sizes (including random sums of random vectors) to multivariate elliptically contoured EP and projective EP laws. The results obtained here give additional theoretical grounds for the applicability of EP and PEP distributions as asymptotic approximations for the statistical regularities observed in data in many fields.

scholarly journals INTERACTION MEASURES ON THE SPACE OF DISTRIBUTIONS OVER THE FIELD OF p-ADIC NUMBERS

2003 ◽  
Vol 06 (03) ◽  
pp. 389-411 ◽  
Author(s):  
ANATOLY N. KOCHUBEI ◽  
MUSTAFA R. SAIT-AMETOV
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Differential Operator ◽  
Dirichlet Boundary ◽  
Dirichlet Boundary Conditions ◽  
Quantum Field ◽  
Pseudo Differential Operator ◽  
Schwartz Distributions ◽  
Space Of Distributions ◽  
Euclidean Quantum Field Theory

We construct measures on the space [Formula: see text], n≤4, of Bruhat–Schwartz distributions over the field of p-adic numbers, corresponding to finite volume polynomial interactions in a p-adic analog of the Euclidean quantum field theory. In contrast to earlier results in this direction, our choice of the free measure is the Gaussian measure corresponding to an elliptic pseudo-differential operator over [Formula: see text]. Analogs of the Euclidean P(φ)-theories with free and half-Dirichlet boundary conditions are considered.

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