scholarly journals On best restricted range approximation in continuous complex-valued function spaces

2005 ◽  
Vol 136 (2) ◽  
pp. 159-181 ◽  
Author(s):  
Chong Li ◽  
K.F. Ng
Keyword(s):  
Function Spaces ◽  
Restricted Range ◽  
Continuous Complex ◽  
Complex Valued

scholarly journals POINTWISE CONVERGENCE AND SEMIGROUPS ACTING ON VECTOR-VALUED FUNCTIONS

2011 ◽  
Vol 84 (1) ◽  
pp. 44-48 ◽  
Author(s):  
MICHAEL G. COWLING ◽  
MICHAEL LEINERT
Keyword(s):  
Banach Space ◽  
Pointwise Convergence ◽  
Function Spaces ◽  
Semigroup Of Operators ◽  
Almost Everywhere ◽  
Vector Valued Function ◽  
Vector Valued Functions ◽  
Complex Valued ◽  
Vector Valued

AbstractA submarkovian C0 semigroup (Tt)t∈ℝ+ acting on the scale of complex-valued functions Lp(X,ℂ) extends to a semigroup of operators on the scale of vector-valued function spaces Lp(X,E), when E is a Banach space. It is known that, if f∈Lp(X,ℂ), where 1<p<∞, then Ttf→f pointwise almost everywhere. We show that the same holds when f∈Lp(X,E) .

Higher Dimensional Spaces of Functions on the Spectrum of a Uniform Algebra

2007 ◽  
Vol 50 (1) ◽  
pp. 3-10
Author(s):  
Richard F. Basener
Keyword(s):  
Continuous Functions ◽  
Uniform Algebra ◽  
Finite Dimensional ◽  
Higher Dimensional ◽  
Spaces Of Continuous Functions ◽  
The Family ◽  
Continuous Complex ◽  
Finite Dimensional Case ◽  
Complex Valued ◽  
Shed Light

AbstractIn this paper we introduce a nested family of spaces of continuous functions defined on the spectrum of a uniform algebra. The smallest space in the family is the uniform algebra itself. In the “finite dimensional” case, from some point on the spaces will be the space of all continuous complex-valued functions on the spectrum. These spaces are defined in terms of solutions to the nonlinear Cauchy–Riemann equations as introduced by the author in 1976, so they are not generally linear spaces of functions. However, these spaces do shed light on the higher dimensional properties of a uniform algebra. In particular, these spaces are directly related to the generalized Shilov boundary of the uniform algebra (as defined by the author and, independently, by Sibony in the early 1970s).

scholarly journals CONDITIONS FOR SOLVABILITY OF THE HARTMAN–WINTNER PROBLEM IN TERMS OF COEFFICIENTS

2003 ◽  
Vol 46 (3) ◽  
pp. 687-702
Author(s):  
N. A. Chernyavskaya ◽  
L. Shuster
Keyword(s):  
Asymptotic Integration ◽  
Subject Classification ◽  
Continuous Complex ◽  
Complex Valued ◽  
Sufficiency Conditions

AbstractThe Equation (1) $(r(x)y')'=q(x)y(x)$ is regarded as a perturbation of (2) $(r(x)z'(x))'=q_1(x)z(x)$. The functions $r(x)$, $q_1(x)$ are assumed to be continuous real valued, $r(x)>0$, $q_1(x)\ge0$, whereas $q(x)$ is continuous complex valued. A problem of Hartman and Wintner regarding the asymptotic integration of (1) for large $x$ by means of solutions of (2) is studied. Sufficiency conditions for solvability of this problem expressed by means of coefficients $r(x)$, $q(x)$, $q_1(x)$ of Equations (1) and (2) are obtained.AMS 2000 Mathematics subject classification: Primary 34E20

On Operators and Distributions

1968 ◽  
Vol 11 (1) ◽  
pp. 61-64 ◽  
Author(s):  
Raimond A. Struble
Keyword(s):  
Commutative Ring ◽  
Operational Calculus ◽  
Delta Function ◽  
Generalized Functions ◽  
Dirac Delta Function ◽  
Quotient Field ◽  
Dirac Delta ◽  
The Family ◽  
Continuous Complex ◽  
Complex Valued

Mikusinski [1] has extended the operational calculus by methods which are essentially algebraic. He considers the family C of continuous complex valued functions on the half-line [0,∞). Under addition and convolution C becomes a commutative ring. Titchmarsh's theorem [2] shows that the ring has no divisors of zero and, hence, that it may be imbedded in its quotient field Q whose elements are then called operators. Included in the field are the integral, differential and translational operators of analysis as well as certain generalized functions, such as the Dirac delta function. An alternate approach [3] yields a rather interesting result which we shall now describe briefly.

Spectral synthesis on zero-dimensional locally compact Abelian groups

2019 ◽  
pp. 450-456
Author(s):  
Sergey S. Platonov
Keyword(s):  
Invariant Subspace ◽  
Linear Subspace ◽  
Spectral Synthesis ◽  
Linear Span ◽  
Locally Compact Abelian Group ◽  
Locally Compact ◽  
Closed Linear Subspace ◽  
Compact Abelian Groups ◽  
Continuous Complex ◽  
Complex Valued

Let G be a zero-dimensional locally compact Abelian group whose elements are compact, C(G) the space of continuous complex-valued functions on the group G. A closed linear subspace H⊆ C(G) is called invariant subspace, if it is invariant with respect to translations τ_y ∶ f(x) ↦ f(x + y), y ∈ G. We prove that any invariant subspace H admits spectral synthesis, which means that H coincides with the closure of the linear span of all characters of the group G contained in H.

Almost transitivity in CoL

1997 ◽  
Vol 121 (1) ◽  
pp. 75-80 ◽  
Author(s):  
P. GREIM ◽  
M. RAJAGOPALAN
Keyword(s):  
Function Spaces ◽  
Complex Valued

Real-valued function spaces CoL lack almost transitive norms. If there is a complex-valued CoL with almost transitive norm then there is also one with transitive norm. We give fairly restrictive topological conditions for the complex-valued CoL to have transitive norm.

scholarly journals Some Results On The Asymptotic Behavior Of Linear Systems

1955 ◽  
Vol 7 ◽  
pp. 531-538 ◽  
Author(s):  
M. Marcus
Keyword(s):  
Differential Equation ◽  
Asymptotic Behavior ◽  
Matrix Differential Equation ◽  
Complex Matrix ◽  
Continuous Complex ◽  
Matrix Differential ◽  
Image Position ◽  
Vector Matrix ◽  
Complex Valued ◽  
Square Complex

1. Introduction. We consider first in §2 the asymptotic behavior as t → ∞ of the solutions of the vector-matrix differential equation(1.1) ,where A is a constant n-square complex matrix, B{t) a continuous complex valued n-square matrix defined on [0, ∞ ), and x a complex n-vector.

Sign in / Sign up

Export Citation Format

Share Document