A Characterization of Totally Real Carleman Sets and an Application to Products of Stratified Totally Real Sets

2016 ◽  
Vol 118 (2) ◽  
pp. 285 ◽  
Author(s):  
Benedikt S. Magnusson ◽  
Erlend Fornæss Wold
Keyword(s):  
Entire Functions ◽  
Carleman Approximation ◽  
Totally Real

We give a characterization of stratified totally real sets that admit Carleman approximation by entire functions. As an application we show that the product of two stratified totally real Carleman sets is a Carleman set.

Carleman Approximation by Entire Functions on the Union of Two Totally Real Subspaces of Cn

1994 ◽  
Vol 37 (4) ◽  
pp. 522-526
Author(s):  
Per E. Manne
Keyword(s):  
Entire Functions ◽  
Continuous Functions ◽  
Real Dimension ◽  
Carleman Approximation ◽  
Polynomially Convex ◽  
Cauchy Riemann ◽  
Totally Real

AbstractLet L1, L2 ⊂ Cn be two totally real subspaces of real dimension n, and such that L1 ∩ L2 = {0}. We show that continuous functions on L1 ∪L2 allow Carleman approximation by entire functions if and only if L1 ∪L2 is polynomially convex. If the latter condition is satisfied, then a function f:L1 ∪L2 —> C such that f|LiCk(Li), i = 1,2, allows Carleman approximation of order k by entire functions if and only if f satisfies the Cauchy-Riemann equations up to order k at the origin.

Characterization of real entire functions by means of their stationary values

1991 ◽  
Vol 56 (3) ◽  
pp. 278-280
Author(s):  
Gundorph K. Kristiansen
Keyword(s):  
Entire Functions

scholarly journals Generalized Order and Best Approximation of Entire Function in -Norm

2010 ◽  
Vol 2010 ◽  
pp. 1-15 ◽  
Author(s):  
Mohammed Harfaoui
Keyword(s):  
Entire Function ◽  
Polynomial Approximation ◽  
Best Approximation ◽  
Extremal Function ◽  
Entire Functions ◽  
Complex Variables ◽  
Several Complex Variables ◽  
Best Polynomial Approximation ◽  
Growth Of Entire Functions

The aim of this paper is the characterization of the generalized growth of entire functions of several complex variables by means of the best polynomial approximation and interpolation on a compact with respect to the set , where is the Siciak extremal function of a -regular compact .

scholarly journals Ricci Curvature for Warped Product Submanifolds of Sasakian Space Forms and Its Applications to Differential Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-15 ◽  
Author(s):  
Fatemah Mofarreh ◽  
Akram Ali ◽  
Nadia Alluhaibi ◽  
Olga Belova
Keyword(s):  
Warped Product ◽  
Necessary Conditions ◽  
Beltrami Operator ◽  
Warping Function ◽  
First Eigenvalue ◽  
Order Ordinary Differential Equation ◽  
Space Forms ◽  
Sasakian Space Forms ◽  
Totally Real

In the present paper, we establish a Chen–Ricci inequality for a C-totally real warped product submanifold M n of Sasakian space forms M 2 m + 1 ε . As Chen–Ricci inequality applications, we found the characterization of the base of the warped product M n via the first eigenvalue of Laplace–Beltrami operator defined on the warping function and a second-order ordinary differential equation. We find the necessary conditions for a base B of a C-totally real-warped product submanifold to be an isometric to the Euclidean sphere S p .

scholarly journals NECESSARY CONDITIONS FOR VECTOR-VALUED OPERATOR INEQUALITIES IN HARMONIC ANALYSIS

2006 ◽  
Vol 93 (2) ◽  
pp. 447-473 ◽  
Author(s):  
MICHAEL CHRIST ◽  
ANDREAS SEEGER
Keyword(s):  
Harmonic Analysis ◽  
Necessary Conditions ◽  
Entire Functions ◽  
Square Functions ◽  
Operator Inequalities ◽  
Functions Of Exponential Type ◽  
Random Construction ◽  
Families Of Operators ◽  
Vector Valued

Via a random construction we establish necessary conditions for $L^p (\ell^q)$ inequalities for certain families of operators arising in harmonic analysis. In particular, we consider dilates of a convolution kernel with compactly supported Fourier transform, vector maximal functions acting on classes of entire functions of exponential type, and a characterization of Sobolev spaces by square functions and pointwise moduli of smoothness.

On a Characterization of Maximal Ideals

1970 ◽  
Vol 13 (2) ◽  
pp. 219-220
Author(s):  
Jamil A. Siddiqi
Keyword(s):  
Banach Algebra ◽  
Maximal Ideal ◽  
Analytic Functions ◽  
Entire Functions ◽  
Factorization Theorem ◽  
Codimension One ◽  
Complex Banach Algebra ◽  
Maximal Ideals ◽  
Invertible Elements

Let A be a commutative complex Banach algebra with identity e. Gleason [1] (cf. also Kahane and Żelazko [2]) has given the following characterization of maximal ideals in A.Theorem. A subspace X ⊂ A of codimension one is a maximal ideal in A if and only if it consists of non-invertible elements.The proofs given by Gleason and by Kahane and Żelazko are both based on the use of Hadamard's factorization theorem for entire functions. In this note we show that this can be avoided by using elementary properties of analytic functions.

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