CLOSURE OF FINITE FUNCTIONS IN ONE WEIGHT SOBOLEV TYPE SPACE

2020 ◽  
Vol 69 (1) ◽  
pp. 12-17
Author(s):  
A. Adiyeva ◽  
◽  
A.O. Baiarystanov ◽  
Keyword(s):  
Weighted Space ◽  
Functional Space ◽  
Second Order ◽  
Weight Space ◽  
Sobolev Type ◽  
Space Theory ◽  
Smooth Functions ◽  
Type Space ◽  
Sobolev Weighted Space ◽  
Smooth Functional

The description of the closure of finite or smooth finite functions in functional spaces are classical tasks of functional space theory. This task is important in smooth functional spaces such as those of Sobolev, Nikolski, Besov and in their various generalizations. Usually, in a weightless space of smooth functions, the set of compactly finite functions, generally speaking, is not dense. But in the weighted space of smooth functions, for example, in the Sobolev weighted space, with strong degeneracy of the weight, many compactly finite functions can be dense. Therefore, an important issue is the problem of characterizing the closure of compactly finite functions in the weight space under consideration. Here we consider a weighted space of Sobolev type of the second order with three weights and it describes the closure of the set of functions with compact supports.

On the Solvability of the Multidimensional Version of the First Darboux Problem for a Model Second-Order Degenerating Hyperbolic Equation

1997 ◽  
Vol 4 (4) ◽  
pp. 341-354
Author(s):  
S. Kharibegashvili
Keyword(s):  
Hyperbolic Equation ◽  
Weighted Space ◽  
Second Order ◽  
Darboux Problem ◽  
Negative Norm ◽  
Correct Formulation ◽  
Sobolev Weighted Space

Abstract A multidimensional version of the first Darboux problem is considered for a model second order degenerating hyperbolic equation. Using the technique of functional spaces with a negative norm, the correct formulation of this problem in the Sobolev weighted space is proved.

scholarly journals Improving KKM Theory on General Metric Type Spaces

2021 ◽  
Vol 9 (1) ◽  
pp. 1-12
Author(s):  
Sehie Park
Keyword(s):  
Convex Space ◽  
Metric Spaces ◽  
Space Theory ◽  
Type Space ◽  
Generalized Metric ◽  
Abstract Convex Space ◽  
Type Spaces

Abstract A generalized metric type space is a generic name for various spaces similar to hyperconvex metric spaces or extensions of them. The purpose of this article is to introduce some KKM theoretic works on generalized metric type spaces and to show that they can be improved according to our abstract convex space theory. Most of these works are chosen on the basis that they can be improved by following our theory. Actually, we introduce abstracts of each work or some contents, and add some comments showing how to improve them.

Random exponential attractor for second-order nonautonomous stochastic lattice systems with multiplicative white noise

2019 ◽  
Vol 19 (06) ◽  
pp. 1950044
Author(s):  
Haijuan Su ◽  
Shengfan Zhou ◽  
Luyao Wu
Keyword(s):  
White Noise ◽  
Weighted Space ◽  
Sufficient Conditions ◽  
Second Order ◽  
Lattice System ◽  
Exponential Attractor ◽  
Lattice Systems ◽  
Random System ◽  
Multiplicative White Noise ◽  
Infinite Sequences

We studied the existence of a random exponential attractor in the weighted space of infinite sequences for second-order nonautonomous stochastic lattice system with linear multiplicative white noise. Firstly, we present some sufficient conditions for the existence of a random exponential attractor for a continuous cocycle defined on a weighted space of infinite sequences. Secondly, we transferred the second-order stochastic lattice system with multiplicative white noise into a random lattice system without noise through the Ornstein–Uhlenbeck process, whose solutions generate a continuous cocycle on a weighted space of infinite sequences. Thirdly, we estimated the bound and tail of solutions for the random system. Fourthly, we verified the Lipschitz continuity of the continuous cocycle and decomposed the difference between two solutions into a sum of two parts, and carefully estimated the bound of the norm of each part and the expectations of some random variables. Finally, we obtained the existence of a random exponential attractor for the considered system.

On the spectra of non-self-adjoint realisations of second-order elliptic operators

1981 ◽  
Vol 90 (1-2) ◽  
pp. 71-105 ◽  
Author(s):  
W. D. Evans
Keyword(s):  
Spherical Shell ◽  
Essential Spectrum ◽  
Weighted Space ◽  
Elliptic Operators ◽  
Second Order ◽  
Sectorial Operator ◽  
Image Position ◽  
Second Order Elliptic Operators ◽  
Complex Valued

SynopsisLet τ denote the second-order elliptic expressionwhere the coefficients bj and q are complex-valued, and let Ω be a spherical shell Ω = {x:x ∈ ℝn, l <|x|<m} with l≧0, m≦∞. Under the conditions assumed on the coefficients of τ and with either Dirichlet or Neumann conditions on the boundary of Ω, τ generates a quasi-m-sectorial operator T in the weighted space L2(Ω;w). The main objective is to locate the spectrum and essential spectrum of T. Best possible results are obtained.

Uniform Boundedness of Lagrange Operator in Some Weighted Sobolev-Type Space

1997 ◽  
Vol 187 (1) ◽  
pp. 61-77 ◽  
Author(s):  
Maria Rosaria Capobianco ◽  
Giuseppe Mastroianni
Keyword(s):  
Uniform Boundedness ◽  
Sobolev Type ◽  
Type Space

scholarly journals Stein's method for negatively associated random variables with applications to second-order stationary random fields

2018 ◽  
Vol 55 (1) ◽  
pp. 196-215 ◽  
Author(s):  
Nathakhun Wiroonsri
Keyword(s):  
Normal Distribution ◽  
Random Vector ◽  
Random Fields ◽  
Second Order ◽  
Multidimensional Case ◽  
Standard Normal Distribution ◽  
Smooth Functions ◽  
Negatively Associated ◽  
Standard Normal ◽  
Stationary Random Fields

Abstract Let ξ = (ξ1, . . ., ξm) be a negatively associated mean-zero random vector with components that obey the bound |ξi| ≤ B, i = 1, . . ., m, and whose sum W = ∑i=1mξi has variance 1. The bound d1(ℒ(W), ℒ(Z)) ≤ 5B - 5.2∑i≠ jσij is obtained, where Z has the standard normal distribution and d1(∙, ∙) is the L1 metric. The result is extended to the multidimensional case with the L1 metric replaced by a smooth functions metric. Applications to second-order stationary random fields with exponential decreasing covariance are also presented.

Sign in / Sign up

Export Citation Format

Share Document