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Displaying 361 – 380 of 452

Semigroup commutators under differences (II).

Nicholas Th. Varopoulos (1993)

Revista Matemática Iberoamericana

This is the second instalment of my previous paper with the same title, [1]. This paper consists of two different parts. The first part is devoted to improvements of the results developed in [1]. These improvements are described in section 0.1 below and developed in sections 1 to 5, and 9 to 10; they are in fact technically distinct from [1] and rely on a systematic use of microlocalisation in the context of Hörmander-Weyl calculus. These paragraphs can therefore be read quite independently from...

Semigroup formulation and approximation of a linear age-dependent population problem with spatial diffusion.

W. Huyer (1994)

Semigroup forum

Semi-groupes sous-Markoviens engendrés par des opérateurs matriciels.

El-Maati Ouhabaz (1993)

Mathematische Annalen

Semigroups affiliated with algebras of operators

Timothy Randolph, Paul Patterson (1994)

Studia Mathematica

Semigroups and resolvents of bounded variation, imaginary powers and H°° functional calculus.

R. de Laubenfels, K. Boyadzhiev (1992)

Semigroup forum

Semigroups with nonquasianalytic growth

Phóng Vũ (1993)

Studia Mathematica

We study asymptotic behavior of $C_{0}$ -semigroups T(t), t ≥ 0, such that ∥T(t)∥ ≤ α(t), where α(t) is a nonquasianalytic weight function. In particular, we show that if σ(A) ∩ iℝ is countable and Pσ(A*) ∩ iℝ is empty, then $l i m_{t \to \infty} 1 / α (t) ∥ T (t) x ∥ = 0$ , ∀x ∈ X. If, moreover, f is a function in $L_{α}^{1} (ℝ_{+})$ which is of spectral synthesis in a corresponding algebra $L_{α_{1}}^{1} (ℝ)$ with respect to (iσ(A)) ∩ ℝ, then $l i m_{t \to \infty} 1 / α (t) ∥ T (t) f ̂ (T) ∥ = 0$ , where $f ̂ (T) = ʃ_{0}^{\infty} f (t) T (t) d t$ . Analogous results are obtained also for iterates of a single operator. The results are extensions of earlier results of Katznelson-Tzafriri,...

Semilinear Cauchy Problems with Almost Sectorial Operators

Tomasz Dlotko (2007)

Bulletin of the Polish Academy of Sciences. Mathematics

Existence of a mild solution to a semilinear Cauchy problem with an almost sectorial operator is studied. Under additional regularity assumptions on the nonlinearity and initial data we also prove the existence of a classical solution to this problem. An example of a parabolic problem in Hölder spaces illustrates the abstract result.

Semilinear evolution equations of the parabolic type

Jan Bochenek (1999)

Annales Polonici Mathematici

This paper is devoted to the investigation of the abstract semilinear initial value problem du/dt + A(t)u = f(t,u), u(0) = u₀, in the "parabolic" case.

Semilinear integro-differential equations with compact semigroups.

Bahuguna, D., Srivastava, S.K. (1998)

Journal of Applied Mathematics and Stochastic Analysis

Shape-preserving properties and asymptotic behaviour of the semigroup generated by the Black-Scholes operator

Antonio Attalienti, Ioan Rasa (2008)

Czechoslovak Mathematical Journal

The paper is devoted to a careful analysis of the shape-preserving properties of the strongly continuous semigroup generated by a particular second-order differential operator, with particular emphasis on the preservation of higher order convexity and Lipschitz classes. In addition, the asymptotic behaviour of the semigroup is investigated as well. The operator considered is of interest, since it is a unidimensional Black-Scholes operator so that our results provide qualitative information on the...

Sharp estimates for the Ornstein-Uhlenbeck operator

Giancarlo Mauceri, Stefano Meda, Peter Sjögren (2004)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Let $ℒ$ be the Ornstein-Uhlenbeck operator which is self-adjoint with respect to the Gauss measure $γ$ on $ℝ^{d} .$ We prove a sharp estimate of the operator norm of the imaginary powers of $ℒ$ on $L^{p} (γ),$ $1 < p < \infty ...$

Shilov parabolic systems

M. Kostić (2012) Bulletin, Classe des Sciences Mathématiques et Naturelles, Sciences mathématiques

Short-time heat flow and functions of bounded variation in $R^{N}$

Michele Miranda, Diego Pallara, Fabio Paronetto, Marc Preunkert (2007)

Annales de la faculté des sciences de Toulouse Mathématiques

We prove a characterisation of sets with finite perimeter and $B V$ functions in terms of the short time behaviour of the heat semigroup in $R^{N}$ . For sets with smooth boundary a more precise result is shown.

Singular evolution problems, regularization, and applications to physics, engineering, and biology

Günter Lumer (1997)

Banach Center Publications

Slowly changing vectors and the asymptotic finite-dimensionality of an operator semigroup.

Storozhuk, K.V. (2009)

Sibirskij Matematicheskij Zhurnal

Smoothing effect for Schrödinger evolution equation via commutator algebra

Shin-ichi Doi (1996/1997)

Séminaire Équations aux dérivées partielles

Solution semigroup and invariant manifolds for functional equations with infinite delay

Hana Petzeltová (1993)

Mathematica Bohemica

It is proved that parabolic equations with infinite delay generate $C_{0}$ -semigroup on the space of initial conditions, such that local stable and unstable manifolds can be constructed for a fully nonlinear problems with help of usual methods of the theory of parabolic equations.

Some applications of fractional calculus to operator semigroups and functional calculus

José E. Galé (2007)

Banach Center Publications

We survey some recent results on functional calculus for generators of holomorphic semigroups, which have been obtained using versions of fractional derivation of Riemann-Liouville or Weyl type. Such a calculus allows us to give tight estimates even in concrete L¹ examples.

Some condensation theorems for semigroup operators.

Oleg V. Davydov (1993)

Manuscripta mathematica

Some Landau's type inequalities for infinitesimal generators.

H. Kraljevic, J. Pecaric (1990)

Aequationes mathematicae

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