Dichotomy and functional calculi.
Die absolute Stetigkeit des positiven Spektrums der Schwingungsgleichungen mit oszillierendem Hauptteil.
Different types of solvability conditions for differential operators.
Differentiability of perturbed semigroups and delay semigroups
Suppose that A generates a C₀-semigroup T on a Banach space X. In 1953 R. S. Phillips showed that, for each bounded operator B on X, the perturbation A+B of A generates a C₀-semigroup on X, and he considered whether certain classes of semigroups are stable under such perturbations. This study was extended in 1968 by A. Pazy who identified a condition on the resolvent of A which is sufficient for the perturbed semigroups to be immediately differentiable. However, M. Renardy showed in 1995 that immediate...
Differentiability of the g-Drazin inverse
If A(z) is a function of a real or complex variable with values in the space B(X) of all bounded linear operators on a Banach space X with each A(z)g-Drazin invertible, we study conditions under which the g-Drazin inverse is differentiable. From our results we recover a theorem due to Campbell on the differentiability of the Drazin inverse of a matrix-valued function and a result on differentiation of the Moore-Penrose inverse in Hilbert spaces.
Differentiable bundles of subspaces and operators in Banach spaces
Differentiable -functional calculus for certain sums of non-commuting operators
We consider a special class of sums of non-commuting positive operators on L²-spaces and derive a formula for their holomorphic semigroups. The formula enables us to give sufficient conditions for these operators to admit differentiable -functional calculus for 1 ≤ p ≤ ∞. Our results are in particular applicable to certain sub-Laplacians, Schrödinger operators and sums of even powers of vector fields on solvable Lie groups with exponential volume growth.
Differential analysis of matrix convex functions. II.
Differentiation of Banach-space-valued additive processes
Dilatability of sesquilinear form-valued kernels
Dilatations des commutants d'opérateurs pour des espaces de Krein de fonctions analytiques
Soient et deux espaces de Krein de fonctions analytiques dans le disque unité invariants pour l’opérateur de déplacement à gauche et soit un opérateur linéaire continu de dans dont l’adjoint commute avec . Nous étudions les dilatations de qui conservent cette propriété de commutation et pour lesquelles les formes hermitiennes définies par et ont le même nombre de carrés négatifs. Nous obtenons ainsi une version du théorème de dilatation des commutants d’opérateurs dans le cadre...
Dilations of Banach space operator valued functions
Dilations of Hilbert space operators (General theory) [Book]
Dilations of Positive Operators: Construction and Ergodic Theory.
Dilations to systems of matrix units
Dirac Operations with Strongly Singular Potentials. Distinguished Self-Adjoint Extensions Constructed with a Spectral Gap Theorem and Cut-Off-Potentials.
Direct Integrals of Left Hubert Algebras.
Direct sums of irreducible operators
It is known that every operator on a (separable) Hilbert space is the direct integral of irreducible operators, but not every one is the direct sum of irreducible ones. We show that an operator can have either finitely or uncountably many reducing subspaces, and the former holds if and only if the operator is the direct sum of finitely many irreducible operators no two of which are unitarily equivalent. We also characterize operators T which are direct sums of irreducible operators in terms of the...
Dirichlet series and uniform ergodic theorems for linear operators in Banach spaces
We study the convergence properties of Dirichlet series for a bounded linear operator T in a Banach space X. For an increasing sequence of positive numbers and a sequence of functions analytic in neighborhoods of the spectrum σ(T), the Dirichlet series for is defined by D[f,μ;z](T) = ∑n=0∞ e-μnz fn(T), z∈ ℂ. Moreover, we introduce a family of summation methods called Dirichlet methods and study the ergodic properties of Dirichlet averages for T in the uniform operator topology.
Discrete spectra criteria for singular difference operators
We investigate oscillation and spectral properties (sufficient conditions for discreteness and boundedness below of the spectrum) of difference operators B(y)n+k = (-1)nwk n (pk n yk).