Ralph Chill
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View article: Domination of nonlinear semigroups generated by regular, local Dirichlet forms
Domination of nonlinear semigroups generated by regular, local Dirichlet forms Open
In this article we study perturbations of local, nonlinear Dirichlet forms on arbitrary topological measure spaces. As a main result, we show that the semigroup generated by a local, regular, nonlinear Dirichlet form $${\mathcal {E}}$$ d…
View article: Domination of nonlinear semigroups generated by regular, local Dirichlet forms
Domination of nonlinear semigroups generated by regular, local Dirichlet forms Open
In this article we study perturbations of local, nonlinear Dirichlet forms on arbitrary topological measure spaces. We show that the semigroup of a local Dirichlet form \(\mathcal{E}\) dominates the semigroup generated by another functiona…
View article: Domination of semigroups generated by regular forms
Domination of semigroups generated by regular forms Open
We give a representation for regular forms associated with dominated -semigroups which, in turn, characterizes the domination of -semigroups associated with regular forms. In addition, we prove a relationship between the positivity of (dom…
View article: Domination of semigroups on standard forms of von Neumann algebras
Domination of semigroups on standard forms of von Neumann algebras Open
Consider $(T_t)_{t\ge 0}$ and $(S_t)_{t\ge 0}$ as real $C_0$-semigroups generated by closed and symmetric sesquilinear forms on a standard form of a von Neumann algebra. We provide a characterisation for the domination of the semigroup $(T…
View article: Nonuniform stability of damped contraction semigroups
Nonuniform stability of damped contraction semigroups Open
We investigate the stability properties of strongly continuous semigroups generated by operators of the form A-B B * , where A is the generator of a contraction semigroup and B is a possibly unbounded operator.Such systems arise naturally …
View article: Real interpolation of functions with applications to accretive operators on Banach spaces
Real interpolation of functions with applications to accretive operators on Banach spaces Open
We study real interpolation, but instead of interpolating between Banach spaces, we interpolate between general functions taking values in $[0,\infty].$ We show the equivalence of the mean method and the $K$-method and apply the general th…
View article: Note on the Kato property of sectorial forms
Note on the Kato property of sectorial forms Open
We characterise the Kato property of a sectorial form a, defined on a Hilbert space V, with respect to a larger Hilbert space H in terms of two bounded, selfadjoint operators T and Q determined by the imaginary part of a and the embedding …
View article: Analysis of a quasilinear coupled magneto-quasistatic model: solvability and regularity of solutions
Analysis of a quasilinear coupled magneto-quasistatic model: solvability and regularity of solutions Open
We consider a~quasilinear model arising from dynamical magnetization. This model is described by a~magneto-quasistatic (MQS) approximation of Maxwell's equations. Assuming that the medium consists of a~conducting and a~non-conducting part,…
View article: Domination of semigroups generated by regular forms
Domination of semigroups generated by regular forms Open
We give a representation for regular forms associated with dominated $C_0$-semigroups which, in turn, characterises domination of $C_0$-semigroups associated with regular forms. In addition, we prove a relationship between the positivity o…
View article: Note on the Kato property of sectorial forms
Note on the Kato property of sectorial forms Open
We characterise the Kato property of a sectorial form $\mathfrak{a}$, defined on a Hilbert space $V$, with respect to a larger Hilbert space $H$ in terms of two bounded, selfadjoint operators $T$ and $Q$ determined by the imaginary part of…
View article: On the numerical range of second order elliptic operators with mixed\n boundary conditions in $L^p$
On the numerical range of second order elliptic operators with mixed\n boundary conditions in $L^p$ Open
We consider second order elliptic operators with real, nonsymmetric\ncoefficient functions which are subject to mixed boundary conditions. The aim\nof this paper is to provide uniform resolvent estimates for the realizations of\nthese oper…
View article: Non-uniform Stability of Damped Contraction Semigroups
Non-uniform Stability of Damped Contraction Semigroups Open
We investigate the stability properties of strongly continuous semigroups generated by operators of the form $A-BB^\ast$, where $A$ is a generator of a contraction semigroup and $B$ is a possibly unbounded operator. Such systems arise natu…
View article: Interpolation of nonlinear positive or order preserving operators on\n Banach lattices
Interpolation of nonlinear positive or order preserving operators on\n Banach lattices Open
We study the relationship between exact interpolation spaces for positive,\nlinear operators, for order preserving, Lipschitz continuous operators, and for\npositive Gagliardo-Peetre operators, and exact partially $K$-monotone spaces in\ni…
View article: The Kurdyka–Łojasiewicz–Simon inequality and stabilisation in nonsmooth infinite-dimensional gradient systems
The Kurdyka–Łojasiewicz–Simon inequality and stabilisation in nonsmooth infinite-dimensional gradient systems Open
We state and reprove a stabilisation result for solutions of abstract gradient systems associated with nonsmooth energy functions on infinite- dimensional Hilbert spaces. The main feature is the introduction of a convenient topology on the…
View article: Weighted inequalities for singular integral operators on the half-line
Weighted inequalities for singular integral operators on the half-line Open
We prove weighted estimates for singular integral operators which operate on function spaces on a half-line. The class of admissible weights includes Muckenhoupt weights and weights satisfying Sawyer's one-sided conditions. The kernels of …
View article: Extrapolation of $L^p$ maximal regularity for second order Cauchy problems
Extrapolation of $L^p$ maximal regularity for second order Cauchy problems Open
If the second order problem $\ddot u + B\dot u + Au = f$ has $L^p$-maximal regularity for some $p\in (1,\infty )$, then it has $\mathbb E_w$-maximal regularity for every rearrangement invariant Banach function space $\mathbb E$ with Boyd i…
View article: The Kurdyka-{\L}ojasiewicz-Simon inequality and stabilisation in nonsmooth infinite-dimensional gradient systems
The Kurdyka-{\L}ojasiewicz-Simon inequality and stabilisation in nonsmooth infinite-dimensional gradient systems Open
We state and prove a stabilisation result for solutions of abstract gradient systems associated with nonsmooth energy functions on infinite dimensional Hilbert spaces. One feature is that in this general setting the assumption on the range…
View article: The Kurdyka-Łojasiewicz-Simon inequality and stabilisation in nonsmooth infinite-dimensional gradient systems
The Kurdyka-Łojasiewicz-Simon inequality and stabilisation in nonsmooth infinite-dimensional gradient systems Open
We state and prove a stabilisation result for solutions of abstract gradient systems associated with nonsmooth energy functions on infinite dimensional Hilbert spaces. One feature is that in this general setting the assumption on the range…
View article: Weak and strong approximation of semigroups on Hilbert spaces
Weak and strong approximation of semigroups on Hilbert spaces Open
For a sequence of uniformly bounded, degenerate semigroups on a Hilbert space, we compare various types of convergences to a limit semigroup. Among others, we show that convergence of the semigroups, or of the resolvents of the generators,…
View article: Quantified versions of Ingham's theorem
Quantified versions of Ingham's theorem Open
We obtain quantified versions of Ingham’s classical Tauberian theorem and some of its variants by means of a natural modification of Ingham’s own simple proof. As corollaries of the main general results, we obtain quantified decay estimate…
View article: Fine scales of decay of operator semigroups
Fine scales of decay of operator semigroups Open
Motivated by potential applications to partial differential equations, we develop a theory of fine scales of decay rates for operator semigroups. The theory contains, unifies, and extends several notable results in the literature on decay …
View article: Operators $L^1 (\mathbb R_+ )\to X$ and the norm continuity problem for semigroups
Operators $L^1 (\mathbb R_+ )\to X$ and the norm continuity problem for semigroups Open
We present a new method for constructing $C_0$-semigroups for which properties of the resolvent of the generator and continuity properties of the semigroup in the operator-norm topology are controlled simultaneously. It allows us to show t…
View article: Real interpolation with weighted rearrangement invariant Banach function\n spaces
Real interpolation with weighted rearrangement invariant Banach function\n spaces Open
Motivated by recent applications of weighted norm inequalities to maximal\nregularity of first and second order Cauchy problems, we study real\ninterpolation spaces on the basis of general Banach function spaces and, in\nparticular, weight…