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Displaying 281 – 300 of 420

Powers and Logarithms

Przeworska-Rolewicz, Danuta (2004)

Fractional Calculus and Applied Analysis

There are applied power mappings in algebras with logarithms induced by a given linear operator D in order to study particular properties of powers of logarithms. Main results of this paper will be concerned with the case when an algebra under consideration is commutative and has a unit and the operator D satisfies the Leibniz condition, i.e. D(xy) = xDy + yDx for x, y ∈ dom D. Note that in the Number Theory there are well-known several formulae expressed by means of some combinations of powers...

Powers of class $w F (p, r, q)$ operators.

Yuan, Jiangtao, Yang, Changsen (2006)

JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]

Powers of m-isometries

Teresa Bermúdez, Carlos Díaz Mendoza, Antonio Martinón (2012)

Studia Mathematica

A bounded linear operator T on a Banach space X is called an (m,p)-isometry for a positive integer m and a real number p ≥ 1 if, for any vector x ∈ X, $\sum_{k = 0}^{m} {(- 1)}^{k} (\binom{m}{k}) | | T^{k} x {| |}^{p} = 0$ . We prove that any power of an (m,p)-isometry is also an (m,p)-isometry. In general the converse is not true. However, we prove that if $T^{r}$ and $T^{r + 1}$ are (m,p)-isometries for a positive integer r, then T is an (m,p)-isometry. More precisely, if $T^{r}$ is an (m,p)-isometry and $T^{s}$ is an (l,p)-isometry, then $T^{t}$ is an (h,p)-isometry, where t = gcd(r,s) and h = min(m,l)....

Powers of operators

Jaroslav Zemánek (2007)

Banach Center Publications

Powers of $p$ -hyponormal operators.

Aluthge, Ariyadasa, Wang, Derming (1999)

Journal of Inequalities and Applications [electronic only]

Practical Ulam-Hyers-Rassias stability for nonlinear equations

Jin Rong Wang, Michal Fečkan (2017)

Mathematica Bohemica

In this paper, we offer a new stability concept, practical Ulam-Hyers-Rassias stability, for nonlinear equations in Banach spaces, which consists in a restriction of Ulam-Hyers-Rassias stability to bounded subsets. We derive some interesting sufficient conditions on practical Ulam-Hyers-Rassias stability from a nonlinear functional analysis point of view. Our method is based on solving nonlinear equations via homotopy method together with Bihari inequality result. Then we consider nonlinear equations...

Preassigning eigenvalues and zeros of nuclear operators

R. Kaiser, J. Retherford (1985)

Studia Mathematica

Precise estimates on the rate at which certain diffusions tend to equilibrium.

L. Saloff-Coste (1994)

Mathematische Zeitschrift

Precompactness in the uniform ergodic theory

Yu. Lyubich, J. Zemánek (1994)

Studia Mathematica

We characterize the Banach space operators T whose arithmetic means ${n^{- 1} (I + T + . . . + T^{n - 1})}_{n \geq 1}$ form a precompact set in the operator norm topology. This occurs if and only if the sequence ${n^{- 1} T^{n}}_{n \geq 1}$ is precompact and the point 1 is at most a simple pole of the resolvent of T. Equivalent geometric conditions are also obtained.

Preconditioners and Korovkin-type theorems for infinite-dimensional bounded linear operators via completely positive maps

K. Kumar, M. N. N. Namboodiri, S. Serra-Capizzano (2013)

Studia Mathematica

The classical as well as noncommutative Korovkin-type theorems deal with the convergence of positive linear maps with respect to different modes of convergence, like norm or weak operator convergence etc. In this article, new versions of Korovkin-type theorems are proved using the notions of convergence induced by strong, weak and uniform eigenvalue clustering of matrix sequences with growing order. Such modes of convergence were originally considered for the special case of Toeplitz matrices and...

Preface

Zbigniew Bartosiewicz, Ewa Girejko (2006)

Control and Cybernetics

Preface

(1999)

Nonlinear Analysis, Function Spaces and Applications

Preface

Krbec, Miroslav, Kufner, Alois, Opic, Bohumír, Rákosník, Jiří (1990)

Nonlinear Analysis, Function Spaces and Applications

Preface

(1994)

Nonlinear Analysis, Function Spaces and Applications

Preface

Fučík, Svatopluk, Kufner, Alois (1979)

Nonlinear Analysis, Function Spaces and Applications

p-representable operators in Banach spaces.

Khalil, Roshdi (1986)

International Journal of Mathematics and Mathematical Sciences

Preservation of ergodicity under perturbation.

I. Fleischer, A. Joffe (1995)

Mathematische Zeitschrift

Preservation of ergodicity under perturbation (Erratum).

I. Fleischer, A. Joffe (1995)

Mathematische Zeitschrift

Preservation of exponential stability for equations with several delays

Leonid Berezansky, Elena Braverman (2011)

Mathematica Bohemica

We consider preservation of exponential stability for the scalar nonoscillatory linear equation with several delays $\dot{x} (t) + \sum_{k = 1}^{m} a_{k} (t) x (h_{k} (t)) = 0, a_{k} (t) \geq 0$ under the addition of new terms and a delay perturbation. We assume that the original equation has a positive fundamental function; our method is based on Bohl-Perron type theorems. Explicit stability conditions are obtained.

Preservation of tensor sum and tensor product.

Kubrusly, C.S., Levan, N. (2011)

Acta Mathematica Universitatis Comenianae. New Series

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