On topologies and boundaries in potential theory. Enlarged ed. of a course of lectures delivered in 1966
From MaRDI portal
Publication:2547643
zbMath0222.31014MaRDI QIDQ2547643
Publication date: 1971
Published in: Lecture Notes in Mathematics (Search for Journal in Brave)
Martin boundary theory (31C35) Introductory exposition (textbooks, tutorial papers, etc.) pertaining to potential theory (31-01) Axiomatic potential theory (31D05) Boundary value and inverse problems for harmonic functions in higher dimensions (31B20) Boundary behavior (theorems of Fatou type, etc.) of harmonic functions in two dimensions (31A20)
Related Items
A new type of minimal thinness with respect to the stationary Schrödinger operator and its applications, On variational principles for the generalized principal eigenvalue of second order elliptic operators and some applications, Minimum Riesz energy problems for a condenser with touching plates, Retracted: Sharp geometrical properties of \(a\)-rarefied sets via fixed point index for the Schrödinger operator equations, Constrained energy problems with external fields for vector measures, Keldysh theorem in Bauer's axiomatic theory of harmonic functions, Harmonic dimensions of covering surfaces, Introduction axiomatique de l'effilement, Une classe de domaines pseudoconvexes. (A class of pseudoconvex domains), A Generalization of the Riesz-Herglotz Theorem on Representing Measures, Fine and Parabolic Limits for Solutions of Second-Order Linear Parabolic Equations on an Infinite Slab, On the spectrum and Martin boundary of homogeneous spaces, On a Problem of Doob About the Fine Topology and Normal Functions, The pluri-fine topology is locally connected, Compactifications of horospheric products, Fine topology and quasilinear elliptic equations, Harmonic dimension of covering surfaces. II, The Cartan, Choquet and Kellogg properties for the fine topology on metric spaces, Fine limits of superharmonic functions, Harmonic measure, equilibrium measure, and thinness at infinity in the theory of Riesz potentials, Preorders on subharmonic functions and measures with applications to the distribution of zeros of holomorphic functions, Parallel subtraction of nonnegative forms, Constrained minimum Riesz energy problems for a condenser with intersecting plates, Criteria of Wiener type for minimally thin sets and rarefied sets associated with the stationary Schrödinger operator in a cone, Sur un théorème de prolongement fonctionnel de Keldych concernant le problème de Dirichlet, Asymptotic behaviour of \(p\) th means of analytic and subharmonic functions in the unit disc and angular distribution of zeros, Riesz-Martin representation for positive super-polyharmonic functions in a Riemannian manifold, New criteria for minimal thinness and rarefiedness associated with cylindrical Schrödinger operator and their geometrical properties, A regular metrizable boundary for solutions of elliptic and parabolic differential equations, Equilibrium problems for infinite dimensional vector potentials with external fields, Ensembles singuliers associés aux espaces de Banach réticulés, An intuitive approach to the Martin boundary, Symmetric function kernels and sweeping of measures, A concept of weak Riesz energy with application to condensers with touching plates, Boundedness of a variation of the positive harmonic function along the normals to the boundary, A construction of representing measures for elliptic and parabolic differential equations, Interior capacities of condensers in locally compact spaces, Green kernels associated with Riesz kernels, On the role of the point at infinity in Deny's principle of positivity of mass for Riesz potentials, Fine topology and estimates for potentials and subharmonic functions, The geometry of \(m\)-hyperconvex domains, Volume mean densities for the heat equation, A theory of inner Riesz balayage and its applications, Amenability and Superharmonic Functions, Criterion of Wiener type for minimal thinness on covering surfaces, Brownian motion on treebolic space: positive harmonic functions, Some characterizations of minimally thin sets in a cylinder and Beurling-Dahlberg-Sjögren type theorems, Martin boundary of unlimited covering surfaces, Fine continuity on metric spaces, Estimates and structure of \(\alpha\)-harmonic functions, Potential analysis for a class of diffusion equations: a Gaussian bounds approach, Various concepts of Riesz energy of measures and application to condensers with touching plates, RETRACTED: Minimally thin sets associated with the stationary Schrödinger operator, Condensers with touching plates and constrained minimum Riesz and Green energy problems, Sur un balayage interieur et les ensembles interieurement effiles, en théorie axiomatique, Markov processes and harmonic spaces, Applications of nonstandard analysis to ideal boundaries in potential theory, On the Martin compactification of a bounded Lipschitz domain in a Riemannian manifold, Removability of the logarithmic singularity for the elliptic PDEs with measurable coefficients and its consequences, Necessary and sufficient conditions for the solvability of the Gauss variational problem for infinite dimensional vector measures, Das Picard-Prinzip und verwandte Fragen bei Störungen von harmonischen Räumen, Uniqueness Theorems for Subharmonic Functions in Unbounded Domains, On Harmonic Majorization of the Martin Function at Infinity in a Cone, Condensers with infinitely many touching Borel plates and minimum energy problems, Subsequences of zeros for classes of holomorphic functions, their stability, and the entropy of arcwise connectedness. I, Resolutive ideal boundaries of nonlinear resistive networks, boundary growth theorems for superharmonic functions, On approximation of affine Baire-one functions, Shape optimization for Dirichlet problems: Relaxed formulation and optimality conditions, A new proof of Drasin's theorem on meromorphic functions of finite order with maximal deficiency sum. II, A new proof of Drasin's theorem on meromorphic functions of finite order with maximal deficiency sum. I, The quasi topology associated with a countably subadditive set function, Geometric and Martin boundaries of a Cartan-Hadamard surface, An alternative concept of Riesz energy of measures with application to generalized condensers, On the Martin boundary of rank 1 manifolds with nonpositive curvature, Potential theory and approximation: highlights from the scientific work of Stephen Gardiner, On positive solutions of second-order elliptic equations, stability results, and classification, Théoreme de Fatou et frontière de Martin, Boundary properties of conformal maps and compactifications of simply connected plane domain, On positivity, criticality, and the spectral radius of the shuttle operator for elliptic operators, Thin sets in nonlinear potential theory, Affine homeomorphisms of Choquet simplexes, Topological countability in Brelot potential theory, Spaces of Baire functions. I, Fine-analytic Functions in C ⁿ, Shilov points and Shilov boundaries, Topological properties of a certain bicompact extension satisfying the first countability axiom, Representations of Hyperharmonic Cones, Fine and quasi connectedness in nonlinear potential theory, On Semiregular Points of the Martin Boundary, Boundary Properties of Minimal Harmonic Functions, On the distribution of zeros of a Ruelle zeta-function, Minimal operators from a potential-theoretic viewpoint, Minimal thinness in an isolated singularity of the Schrödinger equation and application to the Picard principle, The method of extremal length, Unnamed Item, Resistance forms, quasisymmetric maps and heat kernel estimates