2016, London Mathematical Society lecture note series, ISBN 9781107541481, Volume 431., xv, 225 pages

This comprehensive monograph is ideal for established researchers in the field and also graduate students who wish to learn more about the subject. The text is...

Harmonic functions | Subharmonic functions | Hyperbolic spaces

Harmonic functions | Subharmonic functions | Hyperbolic spaces

Book

2011, Graduate studies in mathematics, ISBN 0821853694, Volume 125, xviii, 236

Book

Complex Variables and Elliptic Equations, ISSN 1747-6933, 01/2019, Volume 64, Issue 1, pp. 26 - 39

We define an analogue of the Baernstein star function for a meromorphic function f in several complex variables...

Meromorphic function in several variables | Baernstein star function | subharmonic function | MATHEMATICS | 32A22 | 32A20 | 32A30 | 32A60 | 30D35 | SUBHARMONIC FUNCTIONS | Harmonic functions | Meromorphic functions | Complex variables | Functionals | Mathematical analysis

Meromorphic function in several variables | Baernstein star function | subharmonic function | MATHEMATICS | 32A22 | 32A20 | 32A30 | 32A60 | 30D35 | SUBHARMONIC FUNCTIONS | Harmonic functions | Meromorphic functions | Complex variables | Functionals | Mathematical analysis

Journal Article

1976, L.M.S. monographs, ISBN 0123348013, Volume 9, 20, 2 v.

Book

2016, Volume 662.

Conference Proceeding

Lobachevskii Journal of Mathematics, ISSN 1995-0802, 3/2017, Volume 38, Issue 2, pp. 245 - 254

We recall the definition of quasinearly subharmonic functions, point out that this function class includes, among others, subharmonic functions, quasisubharmonic functions, nearly subharmonic...

Geometry | Subharmonic | Algebra | Analysis | nearly subharmonic | quasinearly subharmonic | Mathematics, general | Probability Theory and Stochastic Processes | Mathematics | Mathematical Logic and Foundations

Geometry | Subharmonic | Algebra | Analysis | nearly subharmonic | quasinearly subharmonic | Mathematics, general | Probability Theory and Stochastic Processes | Mathematics | Mathematical Logic and Foundations

Journal Article

1983, Oxford mathematical monographs, ISBN 0198539061, x, 265 p. --

Book

The Journal of geometric analysis, ISSN 1559-002X, 2017, Volume 28, Issue 4, pp. 3196 - 3222

We study the geometry of m-regular domains within the Caffarelli–Nirenberg–Spruck model in terms of barrier functions, envelopes, exhaustion functions, and Jensen measures...

m -subharmonic function | Caffarelli–Nirenberg–Spruck model | Barrier function | Secondary 31B25 | Mathematics | 32F17 | 46A20 | Primary 31C45 | Abstract Harmonic Analysis | 32T35 | 46J10 | Fourier Analysis | 32U10 | Jensen measure | Exhaustion function | Convex and Discrete Geometry | Global Analysis and Analysis on Manifolds | Differential Geometry | Dynamical Systems and Ergodic Theory | 32U05 | m-subharmonic function | DEFINITION | PSEUDOCONVEX DOMAINS | LELONG NUMBER | APPROXIMATION | CONVEXITY | PLURISUBHARMONIC-FUNCTIONS | INEQUALITY | POTENTIAL-THEORY | BOUNDARY-VALUES | Caffarelli-Nirenberg-Spruck model | MATHEMATICS | JENSEN MEASURES

m -subharmonic function | Caffarelli–Nirenberg–Spruck model | Barrier function | Secondary 31B25 | Mathematics | 32F17 | 46A20 | Primary 31C45 | Abstract Harmonic Analysis | 32T35 | 46J10 | Fourier Analysis | 32U10 | Jensen measure | Exhaustion function | Convex and Discrete Geometry | Global Analysis and Analysis on Manifolds | Differential Geometry | Dynamical Systems and Ergodic Theory | 32U05 | m-subharmonic function | DEFINITION | PSEUDOCONVEX DOMAINS | LELONG NUMBER | APPROXIMATION | CONVEXITY | PLURISUBHARMONIC-FUNCTIONS | INEQUALITY | POTENTIAL-THEORY | BOUNDARY-VALUES | Caffarelli-Nirenberg-Spruck model | MATHEMATICS | JENSEN MEASURES

Journal Article

Qualitative theory of dynamical systems, ISSN 1662-3592, 2015, Volume 15, Issue 2, pp. 471 - 479

... differential systems. But there is not a published proof. In this short paper, we prove that for any positive integer k, the kth Melnikov function and the kth averaging...

Averaging method | Melnikov function | Difference and Functional Equations | Mathematics, general | Limit cycle bifurcation | Mathematics | Dynamical Systems and Ergodic Theory | MATHEMATICS | PERIODIC-ORBITS | ORDER | MATHEMATICS, APPLIED | SUBHARMONIC SOLUTIONS | INVARIANT TORI | BIFURCATIONS | VECTOR-FIELDS | DIFFERENTIAL-SYSTEMS

Averaging method | Melnikov function | Difference and Functional Equations | Mathematics, general | Limit cycle bifurcation | Mathematics | Dynamical Systems and Ergodic Theory | MATHEMATICS | PERIODIC-ORBITS | ORDER | MATHEMATICS, APPLIED | SUBHARMONIC SOLUTIONS | INVARIANT TORI | BIFURCATIONS | VECTOR-FIELDS | DIFFERENTIAL-SYSTEMS

Journal Article

Results in Mathematics, ISSN 1422-6383, 12/2019, Volume 74, Issue 4, pp. 1 - 13

In this article, we prove an extension of the mean value theorem and a comparison theorem for subharmonic functions...

measure densities | Hausdorff measure | Mathematics, general | Mathematics | Subharmonic function | Ahlfors–David sets | 31B05 | mean value theorem | comparison theorem | MATHEMATICS | MATHEMATICS, APPLIED | Ahlfors-David sets | Mathematics - Complex Variables

measure densities | Hausdorff measure | Mathematics, general | Mathematics | Subharmonic function | Ahlfors–David sets | 31B05 | mean value theorem | comparison theorem | MATHEMATICS | MATHEMATICS, APPLIED | Ahlfors-David sets | Mathematics - Complex Variables

Journal Article

Complex Variables and Elliptic Equations, ISSN 1747-6933, 06/2018, Volume 63, Issue 6, pp. 783 - 801

Let be a bounded domain, and let f be a real-valued function defined on the whole topological boundary...

approximation | m-subharmonic function | Jensen measure | Secondary: 46A55 | Exhaustion function | Primary: 32U05 | Dirichlet problem | MATHEMATICS | PLURISUBHARMONIC-FUNCTIONS | SIMPLICIAL CONES | Harmonic functions | Mathematical functions | Approximation | Mathematical analysis

approximation | m-subharmonic function | Jensen measure | Secondary: 46A55 | Exhaustion function | Primary: 32U05 | Dirichlet problem | MATHEMATICS | PLURISUBHARMONIC-FUNCTIONS | SIMPLICIAL CONES | Harmonic functions | Mathematical functions | Approximation | Mathematical analysis

Journal Article

1992, Advances in Soviet mathematics, ISBN 9780821841105, Volume 11, vii, 275

Book

ANNALES POLONICI MATHEMATICI, ISSN 0066-2216, 2019, Volume 123, Issue 1, pp. 21 - 29

We provide a characterization of functions in Cegrell's energy class E-p,E-m.

MATHEMATICS | Cegrell classes | ENERGY | m-subharmonic functions | complex Hessian operator

MATHEMATICS | Cegrell classes | ENERGY | m-subharmonic functions | complex Hessian operator

Journal Article

Sbornik: Mathematics, ISSN 1064-5616, 02/2009, Volume 200, Issue 1-2, pp. 283 - 312

Let Lambda = {lambda(k)} be a sequence of points in the complex plant C and integral a non-trivial entire function of finite order rho and finite type sigma such that integral = 0 on Lambda...

entire function | MATHEMATICS | radius of completeness | system of exponentials | zero sequence | subharmonic function

entire function | MATHEMATICS | radius of completeness | system of exponentials | zero sequence | subharmonic function

Journal Article

Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, 9/2014, Volume 51, Issue 1, pp. 343 - 362

We study harmonic functions on general weighted graphs which allow for a compatible intrinsic metric. We prove an $$L^{p...

Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | 58E20 | Analysis | Theoretical, Mathematical and Computational Physics | Mathematics | 31C05 | MATHEMATICS | MATHEMATICS, APPLIED | METRIC-SPACES | MAPS | STOCHASTIC COMPLETENESS | RANDOM-WALKS | INFINITE-GRAPHS | DIRICHLET FORMS | RECURRENCE | RIEMANNIAN-MANIFOLDS | SUBHARMONIC FUNCTIONS | CONSERVATIVENESS | Harmonic functions | Harmonics | Theorems | Texts | Graphs | Generators | Criteria | Estimates

Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | 58E20 | Analysis | Theoretical, Mathematical and Computational Physics | Mathematics | 31C05 | MATHEMATICS | MATHEMATICS, APPLIED | METRIC-SPACES | MAPS | STOCHASTIC COMPLETENESS | RANDOM-WALKS | INFINITE-GRAPHS | DIRICHLET FORMS | RECURRENCE | RIEMANNIAN-MANIFOLDS | SUBHARMONIC FUNCTIONS | CONSERVATIVENESS | Harmonic functions | Harmonics | Theorems | Texts | Graphs | Generators | Criteria | Estimates

Journal Article

Lobachevskii Journal of Mathematics, ISSN 1995-0802, 1/2017, Volume 38, Issue 1, pp. 38 - 43

... . We build positive subharmonic functions on a part of D vanishing on the boundary ∂D of domain D. We use such (test) functions to study the distribution of zero sets of holomorphic functions f on D...

Geometry | Algebra | holomorphic function | zero set | Analysis | Mathematics, general | Probability Theory and Stochastic Processes | convex function | Mathematics | Subharmonic function | Mathematical Logic and Foundations | Riesz measure

Geometry | Algebra | holomorphic function | zero set | Analysis | Mathematics, general | Probability Theory and Stochastic Processes | convex function | Mathematics | Subharmonic function | Mathematical Logic and Foundations | Riesz measure

Journal Article

Problemy Analiza, ISSN 2306-3424, 2018, Volume 7, Issue Special Issue, pp. 12 - 30

We study approximation of subharmonic functions on the complex plane by logarithms of moduli of entire functions...

Subharmonic function | Approximation | Entire function | Riesz measure | entire function | approximation | subharmonic function

Subharmonic function | Approximation | Entire function | Riesz measure | entire function | approximation | subharmonic function

Journal Article

1971, ISBN 0387054790, 2 v. in 1.

Book

The American mathematical monthly, ISSN 0002-9890, 11/2016, Volume 123, Issue 9, pp. 884 - 893

We review and give elementary proofs of Liouville-type properties of harmonic and subharmonic functions in the plane endowed with a complete Riemannian metric, and prove a gap theorem for the possible...

Harmonic functions | Riemann manifold | Riemann surfaces | Mathematical theorems | Inner products | Subharmonics | Mathematical constants | Laplacians | Mathematical vectors | ARTICLES | Curvature | MATHEMATICS | MANIFOLDS | CURVATURE

Harmonic functions | Riemann manifold | Riemann surfaces | Mathematical theorems | Inner products | Subharmonics | Mathematical constants | Laplacians | Mathematical vectors | ARTICLES | Curvature | MATHEMATICS | MANIFOLDS | CURVATURE

Journal Article

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