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We give very short and transparent proofs of extrapolation theorems of Yano type in the framework of Lorentz spaces. The decomposition technique developed in Edmunds-Krbec (2000) enables us to obtain known and new results in a unified manner.

Vasilescu-Martinelli formula for operators in Banach spaces

V. Kordula, V. Müller (1995)

Studia Mathematica

We prove a formula for the Taylor functional calculus for functions analytic in a neighbourhood of the splitting spectrum of an n-tuple of commuting Banach space operators. This generalizes the formula of Vasilescu for Hilbert space operators and is closely related to a recent result of D. W. Albrecht.

Vector and operator trapezoidal type inequalities for continuous functions of selfadjoint operators in Hilbert spaces.

Dragomir, Sever S. (2011)

ELA. The Electronic Journal of Linear Algebra [electronic only]

Vector and operator valued measures as controls for infinite dimensional systems: optimal control

N.U. Ahmed (2008)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper we consider a general class of systems determined by operator valued measures which are assumed to be countably additive in the strong operator topology. This replaces our previous assumption of countable additivity in the uniform operator topology by the weaker assumption. Under the relaxed assumption plus an additional assumption requiring the existence of a dominating measure, we prove some results on existence of solutions and their regularity properties both for linear and semilinear...

Vector ergodic theorem in $L (X) log L (X)$ .

El Berdan, K. (2000)

Acta Mathematica Universitatis Comenianae. New Series

Vector integral equations with discontinuous right-hand side

Filippo Cammaroto, Paolo Cubiotti (1999)

Commentationes Mathematicae Universitatis Carolinae

We deal with the integral equation $u (t) = f (\int_{I} g (t, z) u (z) d z)$ , with $t \in I = [0, 1]$ , $f : 𝐑^{n} \to 𝐑^{n}$ and $g : I \times I \to [0, + \infty [$ . We prove an existence theorem for solutions $u \in L^{\infty} (I, 𝐑^{n})$ where the function $f$ is not assumed to be continuous, extending a result previously obtained for the case $n = 1$ .

Vector spaces over function fields. Vector spaces over analytic function fields being associated to ordinary differential equations.

Palomar Tarancón, J.E. (2000)

Southwest Journal of Pure and Applied Mathematics [electronic only]

Vectors of Gevrey classes and applications

Lions, J. L. (1967)

Differential Equations and Their Applications

Vectors of uniqueness for id/dx

Ralph de Laubenfels (1988)

Studia Mathematica

Vector-valued ergodic theorems for multiparameter additive processes

Ryotaro Sato (1999)

Colloquium Mathematicae

Let X be a reflexive Banach space and (Ω,Σ,μ) be a σ-finite measure space. Let d ≥ 1 be an integer and T=T(u):u=( $u_{1}$ , ... , $u_{d})$ , $u_{i}$ ≥ 0, 1 ≤ i ≤ d be a strongly measurable d-parameter semigroup of linear contractions on $L_{1}$ ((Ω,Σ,μ);X). We assume that to each T(u) there corresponds a positive linear contraction P(u) defined on $L_{1}$ ((Ω,Σ,μ);ℝ) with the property that ∥ T(u)f(ω)∥ ≤ P(u)∥f(·)∥(ω) almost everywhere on Ω for all f ∈ $L_{1}$ ((Ω,Σ,μ);X). We then prove stochastic and pointwise ergodic theorems for a d-parameter...

Vector-valued ergodic theorems for multiparameter Additive processes II

Ryotaro Sato (2003)

Colloquium Mathematicae

Previously we obtained stochastic and pointwise ergodic theorems for a continuous d-parameter additive process F in L₁((Ω,Σ,μ);X), where X is a reflexive Banach space, under the condition that F is bounded. In this paper we improve the previous results by considering the weaker condition that the function $W (\cdot) = e s s s u p {| | F (I) (\cdot) | | : I \subset [0, 1)}^{d}$ is integrable on Ω.

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Displaying 21 – 40 of 62

Variational sum of monotone operators.

Variational theory of set-valued Hammerstein operators in Banach function spaces. The eigenvalue problem

Variational-like inclusions and resolvent equations involving infinite family of set-valued mappings.

Variational-like inequalities for pseudomonotone operators.

Variations on a theme of Beurling.

Variations on Yano's extrapolation theorem.