All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 5 Next

Displaying 81 – 100 of 451

Showing per page

Asymptotic estimates for a perturbation of the linearization of an equation for compressible viscous fluid flow

Gerhard Ströhmer (2008)

Studia Mathematica

We prove a priori estimates for a linear system of partial differential equations originating from the equations for the flow of a barotropic compressible viscous fluid under the influence of the gravity it generates. These estimates will be used in a forthcoming paper to prove the nonlinear stability of the motionless, spherically symmetric equilibrium states of barotropic, self-gravitating viscous fluids with respect to perturbations of zero total angular momentum. These equilibrium states as...

Asymptotics of sums of subcoercive operators

Nick Dungey, A. ter Elst, Derek Robinson (1999)

Colloquium Mathematicae

We examine the asymptotic, or large-time, behaviour of the semigroup kernel associated with a finite sum of homogeneous subcoercive operators acting on a connected Lie group of polynomial growth. If the group is nilpotent we prove that the kernel is bounded by a convolution of two Gaussians whose orders correspond to the highest and lowest orders of the homogeneous subcoercive components of the generator. Moreover we establish precise asymptotic estimates on the difference of the kernel and the...

Automatic extensions of functional calculi

Ralph deLaubenfels (1995)

Studia Mathematica

Given a Banach algebra ℱ of complex-valued functions and a closed, linear (possibly unbounded) densely defined operator A, on a Banach space, with an ℱ functional calculus we present two ways of extending this functional calculus to a much larger class of functions with little or no growth conditions. We apply this to spectral operators of scalar type, generators of bounded strongly continuous groups and operators whose resolvent set contains a half-line. For f in this larger class, one construction...

Boundedness and growth orders of means of discrete and continuous semigroups of operators

Yuan-Chuan Li, Ryotaro Sato, Sen-Yen Shaw (2008)

Studia Mathematica

We discuss implication relations for boundedness and growth orders of Cesàro means and Abel means of discrete semigroups and continuous semigroups of linear operators. Counterexamples are constructed to show that implication relations between two Cesàro means of different orders or between Cesàro means and Abel means are in general strict, except when the space has dimension one or two.

Boundedness properties of resolvents and semigroups of operators

J. van Casteren (1997)

Banach Center Publications

Let T: H → H be an operator in the complex Hilbert space H. Suppose that T is square bounded in average in the sense that there exists a constant M(T) with the property that, for all natural numbers n and for all x ∈ H, the inequality 1 / ( n + 1 ) ∑ j = 0 n ∥ T j x ∥ 2 ≤ M ( T ) 2 ∥ x ∥ 2 is satisfied. Also suppose that the adjoint T* of the operator T is square bounded in average with constant M(T*). Then the operator T is power bounded in the sense that s u p ∥ T i n ∥ : n ∈ ℕ is finite. In fact the following inequality is valid for all n ∈ ℕ: ∥Tn∥ ≤ e M(T)M(T*). Suppose...

C₀-semigroups generated by second order differential operators

Gabriela Raluca Mocanu (2016)

Annales Polonici Mathematici

Let W ( u ) ( x ) = 1 / 2 x a ( 1 - x ) b u ' ' ( x ) with a,b ≥ 2. We consider the C₀-semigroups generated by this operator on the spaces of continuous functions, respectively square integrable functions. The connection between these semigroups together with suitable approximation processes is studied. Also, some qualitative and quantitative properties are derived.

C-Distribution semigroups

Marko Kostić (2008)

Studia Mathematica

A class of C-distribution semigroups unifying the class of (quasi-) distribution semigroups of Wang and Kunstmann (when C = I) is introduced. Relations between C-distribution semigroups and integrated C-semigroups are given. Dense C-distribution semigroups as well as weak solutions of the corresponding Cauchy problems are also considered.

Classes of distribution semigroups

Peer Christian Kunstmann, Modrag Mijatović, Stevan Pilipović (2008)

Studia Mathematica

We introduce various classes of distribution semigroups distinguished by their behavior at the origin. We relate them to quasi-distribution semigroups and integrated semigroups. A class of such semigroups, called strong distribution semigroups, is characterized through the value at the origin in the sense of Łojasiewicz. It contains smooth distribution semigroups as a subclass. Moreover, the analysis of the behavior at the origin involves intrinsic structural results for semigroups. To this purpose,...

Currently displaying 81 – 100 of 451