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Composition operators with closed range on the Dirichlet space
It is well known that the composition operator on Hardy or Bergman space has a closed range if and only if its Nevanlinna counting function induces a...
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Block dual Toeplitz operators on the orthogonal complement of the Dirichlet space
We give some characterizations of block dual Toeplitz operators acting on the orthogonal complement of the Dirichlet space. We characterized the...
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On the Solvability of the Dirichlet Problem for a Multidimensional Elliptic System in the Half-Space
The Dirichlet problem for a multidimensional elliptic system in the half-space is considered. With the help of the Fourier transform, the problem of...
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The Dirichlet Space
The notes below are a copy of a set of three lectures presented online in July 2021, during the Fields Institute Focus Program Analytic Function...
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Overdetermined problems for fully nonlinear equations with constant Dirichlet boundary conditions in space forms
We consider overdetermined problems for two classes of fully nonlinear equations with constant Dirichlet boundary conditions in a bounded domain in...
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Composition operators on the normal weight Dirichlet type space in the unit disc
Let p > 0 and ν be a normal function on [0, 1). In this paper, several equivalent characterizations are given for which composition operators are...
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Complex Symmetry of Linear Combinations of Composition Operators on the McCarthy–Bergman Space of Dirichlet Series
The complex symmetric linear combinations of composition operators on the McCarthy–Bergman spaces of Dirichlet series are completely characterized....
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Chebyshev Subspaces of Dirichlet Series
AbstractHaar and Kolmogorov found the necessary and sufficient conditions under which finite-dimensional subspaces in the space of continuous...
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On the Dirichlet problem for the Schrödinger equation in the upper half-space
A well-known result of Stein-Weiss in 1971 said that a harmonic function, defined on the upper half-space, is the Poisson integral of a Lebesgue...
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Ergodic decompositions of Dirichlet forms under order isomorphisms
We study ergodic decompositions of Dirichlet spaces under intertwining via unitary order isomorphisms. We show that the ergodic decomposition of a...
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Domination of nonlinear semigroups generated by regular, local Dirichlet forms
In this article we study perturbations of local, nonlinear Dirichlet forms on arbitrary topological measure spaces. As a main result, we show that...
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Resonant-Superlinear Nonhomogeneous Dirichlet Problems
We consider a Dirichlet nonlinear equation driven by the ( p , 2)-Laplacian and with a reaction having the competing effects of a parametric asymmetric...
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Weak Dirichlet Processes
An important generalization of the notion of Dirichlet process is the one of weak Dirichlet process that is characterized as the sum of a local...
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