A STRUCTURE THEOREM FOR THE SPACE $({G}^{\alpha}_{\alpha})^{\prime}$

2013 ◽  
Vol 16 (01) ◽  
pp. 1380002
Author(s):  
BISHNU PRASAD DHUNGANA
Keyword(s):  
Dual Space ◽  
Bounded Function ◽  
Structure Theorem ◽  
Continuous Bounded Function ◽  
Laguerre Expansions

For α, β ≥ 1. The space [Formula: see text] is the dual space of [Formula: see text] introduced by Duran in [Laguerre expansions of Gelfand–Shilov spaces, J. Approx. Theory74 (1993)]. We give a structure for the space [Formula: see text], α ≥ 1 as follows: [Formula: see text] if and only if there exist a sequence {bm} ⊂ (0, ∞) and a continuous bounded function f on (0, ∞) such that for every d > 0 there exists a constant C > 0 satisfying [Formula: see text].

scholarly journals On one approach to the approximation of solutions to the direct kinematics problem of parallel manipulators

2020 ◽  
Vol 10 (1) ◽  
pp. 65-70
Author(s):  
Andrei Gorchakov ◽  
Vyacheslav Mozolenko
Keyword(s):  
Neural Network ◽  
Bounded Function ◽  
Parallel Manipulators ◽  
Feedforward Neural Network ◽  
Numerical Implementation ◽  
Continuous Bounded Function ◽  
Space Filling ◽  
Space Filling Curves ◽  
Direct Kinematics

AbstractAny real continuous bounded function of many variables is representable as a superposition of functions of one variable and addition. Depending on the type of superposition, the requirements for the functions of one variable differ. The article investigated one of the options for the numerical implementation of such a superposition proposed by Sprecher. The superposition was presented as a three-layer Feedforward neural network, while the functions of the first’s layer were considered as a generator of space-filling curves (Peano curves). The resulting neural network was applied to the problems of direct kinematics of parallel manipulators.

scholarly journals Homoclinic Solutions for a Class of Second Order Nonautonomous Singular Hamiltonian Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Ziheng Zhang ◽  
Fang-Fang Liao ◽  
Patricia J. Y. Wong
Keyword(s):  
Hamiltonian Systems ◽  
Bounded Function ◽  
Homoclinic Solution ◽  
Second Order ◽  
Homoclinic Solutions ◽  
Global Maximum ◽  
Continuous Bounded Function ◽  
Almost Periodic ◽  
Strong Force ◽  
Singular Hamiltonian Systems

We are concerned with the existence of homoclinic solutions for the following second order nonautonomous singular Hamiltonian systemsu¨+atWuu=0, (HS) where-∞<t<+∞,u=u1,u2, …,uN∈ℝNN≥3,a:ℝ→ℝis a continuous bounded function, and the potentialW:ℝN∖{ξ}→ℝhas a singularity at0≠ξ∈ℝN, andWuuis the gradient ofWatu. The novelty of this paper is that, for the case thatN≥3and (HS) is nonautonomous (neither periodic nor almost periodic), we show that (HS) possesses at least one nontrivial homoclinic solution. Our main hypotheses are the strong force condition of Gordon and the uniqueness of a global maximum ofW. Different from the cases that (HS) is autonomousat≡1or (HS) is periodic or almost periodic, as far as we know, this is the first result concerning the case that (HS) is nonautonomous andN≥3. Besides the usual conditions onW, we need the assumption thata′t<0for allt∈ℝto guarantee the existence of homoclinic solution. Recent results in the literature are generalized and significantly improved.

scholarly journals Structure Theorem for Functionals in the Space

2008 ◽  
Vol 2008 ◽  
pp. 1-9
Author(s):  
Hamed M. Obiedat ◽  
Wasfi A. Shatanawi ◽  
Mohd M. Yasein
Keyword(s):  
Dual Space ◽  
Structure Theorem ◽  
Topological Characterization ◽  
Riesz Representation

We introduce the space of all functions such that and are finite for all , , where and are two weights satisfying the classical Beurling conditions. Moreover, we give a topological characterization of the space without conditions on the derivatives. For functionals in the dual space , we prove a structure theorem by using the classical Riesz representation thoerem.

Central Idempotent Measures on Unitary Groups

1970 ◽  
Vol 22 (4) ◽  
pp. 719-725 ◽  
Author(s):  
Daniel Rider
Keyword(s):  
Bounded Function ◽  
Abelian Groups ◽  
Locally Compact Group ◽  
Unitary Groups ◽  
Compact Groups ◽  
Central Idempotent ◽  
Continuous Bounded Function ◽  
Locally Compact ◽  
Borel Measures ◽  
Image Position

Let G be a locally compact group and M(G) the space of finite regular Borel measures on G. If μ and v are in M(G), their convolution is defined byThus, if f is a continuous bounded function on G,μ is central if μ(Ex) = μ(xE) for all x ∈ G and all measurable sets E. μ is idempotent if μ * μ = μ.The idempotent measures for abelian groups have been classified by Cohen [1]. In this paper we will show that for a certain class of compact groups, containing the unitary groups, the central idempotents can be characterized. The method consists of showing that, in these cases, the central idempotents arise from idempotents on abelian groups and applying Cohen's result.

Semilinear elliptic problems with singular potentials in ℝN

1993 ◽  
Vol 123 (4) ◽  
pp. 593-619
Author(s):  
Marino Badiale ◽  
Nicoletta A. Tchou
Keyword(s):  
Elliptic Problem ◽  
Variational Approach ◽  
Bounded Function ◽  
Structure Theorem ◽  
Existence Theorems ◽  
Singular Potentials ◽  
Lack Of Compactness ◽  
Semilinear Elliptic Problem ◽  
Semilinear Elliptic ◽  
Semilinear Elliptic Problems

SynopsisWe study a semilinear elliptic problem on ℝN where a potential is not a bounded function but can also be an infinite measure. We analyse the lack of compactness of the problem, obtaining a structure theorem for Palais-Smale sequences. This result allows us to obtain different kinds of existence theorems by a variational approach.

Existence

2017 ◽  
Author(s):  
Bernhard M¨uhlherr ◽  
Holger P. Petersson ◽  
Richard M. Weiss
Keyword(s):  
Division Algebra ◽  
Quadratic Forms ◽  
Structure Theorem ◽  
Quadratic Extension ◽  
Quadratic Space ◽  
Division Algebras ◽  
Separable Extension ◽  
Valued Fields ◽  
Quaternion Division Algebra

This chapter proves that Bruhat-Tits buildings exist. It begins with a few definitions and simple observations about quadratic forms, including a 1-fold Pfister form, followed by a discussion of the existence part of the Structure Theorem for complete discretely valued fields due to H. Hasse and F. K. Schmidt. It then considers the generic unramified cases; the generic semi-ramified cases, the generic ramified cases, the wild unramified cases, the wild semi-ramified cases, and the wild ramified cases. These cases range from a unique unramified quadratic space to an unramified separable quadratic extension, a tamely ramified division algebra, a ramified separable quadratic extension, and a unique unramified quaternion division algebra. The chapter also describes ramified quaternion division algebras D₁, D₂, and D₃ over K containing a common subfield E such that E/K is a ramified separable extension.

On Lattice-Ordered Rees Matrix Γ-Semigroups

2013 ◽  
Vol 59 (1) ◽  
pp. 209-218 ◽  
Author(s):  
Kostaq Hila ◽  
Edmond Pisha
Keyword(s):  
Structure Theorem ◽  
Lattice Of Congruences

Abstract The purpose of this paper is to introduce and give some properties of l-Rees matrix Γ-semigroups. Generalizing the results given by Guowei and Ping, concerning the congruences and lattice of congruences on regular Rees matrix Γ-semigroups, the structure theorem of l-congruences lattice of l - Γ-semigroup M = μº(G : I; L; Γe) is given, from which it follows that this l-congruences lattice is distributive.

Sign in / Sign up

Export Citation Format

Share Document