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Displaying 401 – 420 of 452

Stochastic integration of functions with values in a Banach space

J. M. A. M. van Neerven, L. Weis (2005)

Studia Mathematica

Let H be a separable real Hilbert space and let E be a real Banach space. In this paper we construct a stochastic integral for certain operator-valued functions Φ: (0,T) → ℒ(H,E) with respect to a cylindrical Wiener process ${W_{H} (t)}_{t \in [0, T]}$ . The construction of the integral is given by a series expansion in terms of the stochastic integrals for certain E-valued functions. As a substitute for the Itô isometry we show that the square expectation of the integral equals the radonifying norm of an operator which is...

Strong stabilization of controlled vibrating systems

Jean-François Couchouron (2011)

ESAIM: Control, Optimisation and Calculus of Variations

This paper deals with feedback stabilization of second order equations of the form ytt + A0y + u (t) B0y (t) = 0, t ∈ [0, +∞[, where A0 is a densely defined positive selfadjoint linear operator on a real Hilbert space H, with compact inverse and B0 is a linear map in diagonal form. It is proved here that the classical sufficient ad-condition of Jurdjevic-Quinn and Ball-Slemrod with the feedback control u = ⟨yt, B0y⟩H implies the strong stabilization. This result is derived from a general compactness...

Strong stabilization of controlled vibrating systems

Jean-François Couchouron (2011)

ESAIM: Control, Optimisation and Calculus of Variations

Sums of commuting operators with maximal regularity

Christian Le Merdy, Arnaud Simard (2001)

Studia Mathematica

Let Y be a Banach space and let $S \subset L_{p}$ be a subspace of an $L_{p}$ space, for some p ∈ (1,∞). We consider two operators B and C acting on S and Y respectively and satisfying the so-called maximal regularity property. Let ℬ and be their natural extensions to $S (Y) \subset L_{p} (Y)$ . We investigate conditions that imply that ℬ + is closed and has the maximal regularity property. Extending theorems of Lamberton and Weis, we show in particular that this holds if Y is a UMD Banach lattice and $e^{- t B}$ is a positive contraction on $L_{p}$ for any...

Sur les semigroupes dynamiques quantiques

Rolando Rebolledo (1996)

Annales mathématiques Blaise Pascal

Systems of degenerate differential equations in Banach spaces.

Falaleev, M.V., Korobova, O.V. (2008)

Sibirskij Matematicheskij Zhurnal

The adjoint of a positive semigroup

J. M. A. M. Van Neerven, B. de Pagter (1994)

Compositio Mathematica

The Cauchy problem for an inclusion in Banach spaces and distribution spaces.

Mel'nikova, I.V. (2001)

Sibirskij Matematicheskij Zhurnal

The Dirichlet-Neumann operator on continuous functions

Joachim Escher (1994)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

The domain of the Ornstein-Uhlenbeck operator on an $L^{p}$ -space with invariant measure

Giorgio Metafune, Jan Prüss, Abdelaziz Rhandi, Roland Schnaubelt (2002)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

We show that the domain of the Ornstein-Uhlenbeck operator on $L^{p}$ $(ℝ^{N}, μ d x ...$

The formal Laplace--Borel transform of Fliess operators and the composition product.

Li, Yaqin, Gray, W.Steven (2006) International Journal of Mathematics and Mathematical Sciences

The fundamental solutions for fractional evolution equations of parabolic type.

El-Borai, Mahmoud M. (2004) Boletín de la Asociación Matemática Venezolana

The Hardy-Landau-Littlewood inequalities with less smoothness.

Niculescu, Constantin P., Buşe, Constantin (2003) JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]

The Kneser property for the abstract Cauchy problem

Hernán R. Henríquez, Genaro Castillo G. (2003) Annales Polonici Mathematici

We establish existence of mild solutions for the semilinear first order functional abstract Cauchy problem and we prove that the set of mild solutions of this problem is connected in the space of continuous functions.

The martingale problem for a class of pseudo differential operators.

Walter Hoh (1994) Mathematische Annalen

The norm convergence of a Magnus expansion method

András Bátkai, Eszter Sikolya (2012) Open Mathematics

We consider numerical approximation to the solution of non-autonomous evolution equations. The order of convergence of the simplest possible Magnus method is investigated.

The operator equation AX - XB = C with unbounded operators A and B and related abstract Cauchy problems.

Vu Quoc Phóng (1991) Mathematische Zeitschrift

The Ornstein-Uhlenbeck generator perturbed by the gradient of a potential

Giuseppe Da Prato (1998) Bollettino dell'Unione Matematica Italiana

Si considera, in uno spazio di Hilbert

H

l'operatore lineare

M_{0} φ = 1 / 2 Tr [D^{2} φ] + 〈x, A D φ〉 - 〈D U (x), D φ〉

, dove

A

è un operatore negative autoaggiunto e

U

è un potenziale che soddisfa a opportune condizioni di integrabilità. Si dimostra con un metodo analitico che

M_{0}

è essenzialmente autoaggiunto in uno spazio

L^{2} (H, ν)

e si caratterizza il dominio della sua chiusura

M

come sottospazio di

W^{2, 2} (H, ν)

. Si studia inoltre la «spectral gap property» del semigruppo generato da

M

The parabolic mixed Cauchy-Dirichlet problem in spaces of functions which are hölder continuous with respect to space variables

Davide Guidetti (1996)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

We give a new proof, based on analytic semigroup methods, of a maximal regularity result concerning the classical Cauchy-Dirichlet's boundary value problem for second order parabolic equations. More specifically, we find necessary and sufficient conditions on the data in order to have a strict solution $u$ which is bounded with values in $C^{2 + θ} (\bar{Ω})$ (0 < < 1), with $\partial_{t} u$ bounded with values in $C^{θ} (\bar{Ω})$ .

The RAGE theorem in Banach spaces.

J. Kreulich (1994)

Semigroup forum

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