The Cauchy process and the Steklov problem
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Publication:1883227
DOI10.1016/j.jfa.2004.02.005zbMath1055.60072OpenAlexW1973079440MaRDI QIDQ1883227
Rodrigo Bañuelos, Tadeusz Kulczycki
Publication date: 1 October 2004
Published in: Journal of Functional Analysis (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.jfa.2004.02.005
spectral theorynodal setsCauchy processmixed Steklov problemsymmetry properties of eigenfunctionsvariational formula for eigenvalues
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Cites Work
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- Markov operators and their associated semi-groups
- The asymptotic distribution of the eigenvalues for a class of Markov operators
- The first exit time of a two-dimensional symmetric stable process from a wedge
- Stekloffsche Eigenwerte und konforme Abbildungen. (Stekloff eigenvalues and conformal mappings)
- On the nodal line of the second eigenfunction of the Laplacian in \(\mathbb{R}^ 2\)
- On extensions of the Brunn-Minkowski and Prekopa-Leindler theorems, including inequalities for log concave functions, and with an application to the diffusion equation
- Martin boundary and integral representation for harmonic functions of symmetric stable processes
- Estimates on Green functions and Poisson kernels for symmetric stable processes
- Probabilistic proof of boundary Harnack principle for \(\alpha\)-harmonic functions
- Representation of \(a\)-harmonic functions in Lipschitz domains
- A lower bound for the gap between the first two eigenvalues of Schrödinger operators on convex domains in \(\mathbb{S}^ n\) or \(\mathbb{R}^ n\)
- Nodal lines of eigenfunctions of the fixed membrane problem in general convex domains
- Intrinsic ultracontractivity and conditional gauge for symmetric stable processes
- Intrinsic ultracontractivity, conditional lifetimes and conditional gauge for symmetric stable processes on rough domains
- Sharp inequalities for heat kernels of Schrödinger operators and applications to spectral gaps
- Estimates of Green function for relativistic \(\alpha\)-stable process
- On the spectral gap for fixed membranes
- Brascamp-Lieb-Luttinger inequalities for convex domains of finite inradius
- Exit times from cones in \(R^n\) of symmetric stable processes
- Stable processes have thorns
- Boundary Harnack principle for symmetric stable processes
- Diffusion equations and geometric inequalities
- Extreme principles and isoperimetric inequalities for some mixed problems of Stekloff's type
- Pseudo-differential operators and Gevrey classes
- Multi-dimensional diffusion and the Markov process on the boundary
- On some relations between the harmonic measure and the Levy measure for a certain class of Markov processes
- A Brascamp-Lieb-Luttinger–type inequality and applications to symmetric stable processes
- First Passage Times for Symmetric Stable Processes in Space
- Potential theory for the α-stable Schrödinger operator on bounded Lipschitz domains
- The boundary Harnack principle for the fractional Laplacian
- Symmetrization, symmetric stable processes, and Riesz capacities
- Isoperimetric Inequalities and Their Applications
- On the Distribution of First Hits for the Symmetric Stable Processes