Rational Approximations in the Complex Plane for Laplace Transforms of Transcendental Linear Operators

2000 ◽  
pp. 69-89
Author(s):  
Walter J. Freeman
Keyword(s):  
Complex Plane ◽  
Laplace Transforms ◽  
Linear Operators ◽  
Rational Approximations

The Usual Behaviour of Rational Approximations

1983 ◽  
Vol 26 (3) ◽  
pp. 317-323 ◽  
Author(s):  
Peter B. Borwein
Keyword(s):  
Complex Plane ◽  
Metric Space ◽  
Unit Disc ◽  
Entire Functions ◽  
Complete Metric Space ◽  
Point Of View ◽  
Rational Approximations ◽  
Speed Of Convergence ◽  
Entire Plane ◽  
Categorical Point

AbstractQuestions concerning the convergence of Padé and best rational approximations are considered from a categorical point of view in the complete metric space of entire functions. The set of functions for which a subsequence of the mth row of the Padé table converges uniformly on compact subsets of the complex plane is shown to be residual.The speed of convergence of best uniform rational approximations and Padé approximations on the unit disc is compared. It is shown that, in a categorical sense, it is expected that subsequences of these approximants will converge at the same rate.Likewise, it is expected that the poles of certain sequences of best uniform rational approximations wil be dense in the entire plane.

scholarly journals Approximation by partial isometries

1986 ◽  
Vol 29 (2) ◽  
pp. 255-261 ◽  
Author(s):  
Pei Yuan Wu
Keyword(s):  
Hilbert Space ◽  
Complex Plane ◽  
Closed Subset ◽  
Separable Hilbert Space ◽  
Linear Operators ◽  
Unitary Operators ◽  
Nonempty Closed Subset ◽  
Partial Isometries ◽  
Bounded Linear ◽  
Normal Operators

Let B(H) be the algebra of bounded linear operators on a complex separable Hilbert space H. The problem of operator approximation is to determine how closely each operator T ∈B(H) can be approximated in the norm by operators in a subset L of B(H). This problem is initiated by P. R. Halmo [3] when heconsidered approximating operators by the positive ones. Since then, this problem has been attacked with various classes L: the class of normal operators whose spectrum is included in a fixed nonempty closed subset of the complex plane [4], the classes of unitary operators [6] and invertible operators [1]. The purpose of this paper is to study the approximation by partial isometries.

scholarly journals Ideal Convergence ofk-Positive Linear Operators

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Akif Gadjiev ◽  
Oktay Duman ◽  
A. M. Ghorbanalizadeh
Keyword(s):  
Complex Plane ◽  
Connected Domain ◽  
Analytic Functions ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Ideal Convergence ◽  
Simply Connected Domain ◽  
Convergence Results ◽  
Simply Connected

We study some ideal convergence results ofk-positive linear operators defined on an appropriate subspace of the space of all analytic functions on a bounded simply connected domain in the complex plane. We also show that our approximation results with respect to ideal convergence are more general than the classical ones.

scholarly journals On ideal convergence of sequences of linear operators in the space of analytic functions

Filomat ◽  
2016 ◽  
Vol 30 (1) ◽  
pp. 241-251
Author(s):  
Nursel Çetin
Keyword(s):  
Complex Plane ◽  
Connected Domain ◽  
Analytic Functions ◽  
Linear Operators ◽  
Space Of Analytic Functions ◽  
Ideal Convergence ◽  
Simply Connected Domain ◽  
Convergence Of Sequences ◽  
Simply Connected

We investigate the problem of ideal convergence of the sequences of linear operators without the properties of k-positivity in the space of analytic functions in a bounded simply connected domain of complex plane.

scholarly journals Linear operators generated by Sonnenschein matrices

1978 ◽  
Vol 25 (3) ◽  
pp. 375-384 ◽  
Author(s):  
B. Wood
Keyword(s):  
Complex Plane ◽  
Approximation Method ◽  
Linear Operators ◽  
Approximation Process ◽  
The Matrix

AbstractAn approximation method based on a certain Sonnenschein matrix is studied. Results are obtained for approximation in an interval and in the complex plane. A connection between convergence of the approximation process and regularity of the matrix is also discussed.

scholarly journals Direct and converse inequalities for positive linear operators on the positive semi-axis

1999 ◽  
Vol 66 (1) ◽  
pp. 90-103 ◽  
Author(s):  
José A. Adell ◽  
Carmen Sangüesa
Keyword(s):  
Uniform Convergence ◽  
Fractional Derivatives ◽  
Laplace Transforms ◽  
Modulus Of Smoothness ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Poisson Mixtures ◽  
Baskakov Operator ◽  
Probabilistic Type ◽  
Derivatives Of

AbstractWe consider positive linear operators of probabilistic type L1f acting on real functions f defined on the positive semi-axis. We deal with the problem of uniform convergence of L1f to f, both in the usual sup-norm and in a uniform Lp type of norm. In both cases, we obtain direct and converse inequalities in terms of a suitable weighted first modulus of smoothness of f. These results are applied to the Baskakov operator and to a gamma operator connected with real Laplace transforms, Poisson mixtures and Weyl fractional derivatives of Laplace transforms.

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