Results 41 to 50 of about 476,746 (208)

Polynomial Growth Harmonic Functions on Finitely Generated Abelian Groups

, 2013
In the present paper, we develop geometric analytic techniques on Cayley graphs of finitely generated abelian groups to study the polynomial growth harmonic functions.
B Hua, B Hua, B Kleiner, Bobo Hua, C-J Sung, D Burago, DJS Robinson, F Lin, FRK Chung, G Alexopoulos, G Alexopoulos, G Alexopoulos, G Alexopoulos, GF Lawler, H Donnelly, HA Heilbronn, I Holopainen, J Milnor, J Moser, J Wang, Jürgen Jost, L-F Tam, M Gromov, M Suzuki, MS Raghunathan, P Kuchment, P Li, P Li, P Li, P Li, P Li, R Chen, RJ Duffin, ST Yau, ST Yau, SW Kim, SY Cheng, T Coulhon, T Coulhon, T Delmotte, TH Colding, TH Colding, TH Colding, TH Colding, Xianqing Li-Jost, Y Lin, Y Lin, Y Shalom, YH Lee   +48 more
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Harmonic morphisms and subharmonic functions

International Journal of Mathematics and Mathematical Sciences, 2005
Let M be a complete Riemannian manifold and N a complete noncompact Riemannian manifold. Let ϕ:M→N be a surjective harmonic morphism. We prove that if N admits a subharmonic function with finite Dirichlet integral which is not harmonic, and ϕ has finite
Gundon Choi, Gabjin Yun
doaj   +1 more source

Some identities on generalized harmonic numbers and generalized harmonic functions

Demonstratio Mathematica, 2023
The harmonic numbers and generalized harmonic numbers appear frequently in many diverse areas such as combinatorial problems, many expressions involving special functions in analytic number theory, and analysis of algorithms.
Kim Dae San, Kim Hyekyung, Kim Taekyun
doaj   +1 more source

Ruscheweyh-type meromorphic harmonic functions

Journal of Inequalities and Applications
In this paper, we study classes of meromorphic harmonic functions defined by Ruscheweyh derivatives. In addition to finding certain analytic criteria, we obtain radii of starlikeness and convexity, and some topological properties for the defined classes ...
J. Dziok
doaj   +1 more source

Harmonic functions on the real hyperbolic ball I : Boundary values and atomic decomposition of Hardy spaces

, 1999
We study harmonic functions for the Laplace-Beltrami operator on the real hyperbolic ball. We obtain necessary and sufficient conditions for this functions and their normal derivatives to have a boundary distribution.In doing so, we put forward different
Jaming, Philippe
core   +2 more sources

A Path Planning Algorithm for a Dynamic Environment Based on Proper Generalized Decomposition

Mathematics, 2020
A necessity in the design of a path planning algorithm is to account for the environment. If the movement of the mobile robot is through a dynamic environment, the algorithm needs to include the main constraint: real-time collision avoidance.
Antonio Falcó, Lucía Hilario, Nicolás Montés, Marta C. Mora, Enrique Nadal   +4 more
doaj   +1 more source

On α-Harmonic Functions [PDF]

Nagoya Mathematical Journal, 1966
M. Riesz [8] introduced the notion of α-superharmonic functions in n(≥1)-dimensional Euclidean space Rn in connection with the potential of order α. In this paper, we shall first define the α-superharmonic and α-harmonic functions in a domain D. In case α = 2, they coincide with ones in the usual sense.
openaire   +4 more sources

Harmonic functions on multiplicative graphs and interpolation polynomials [PDF]

, 1999
We construct examples of nonnegative harmonic functions on certain graded graphs: the Young lattice and its generalizations. Such functions first emerged in harmonic analysis on the infinite symmetric group.
Borodin, Alexei, Olshanski, Grigori
core   +2 more sources

Harnack Inequality and Regularity for a Product of Symmetric Stable Process and Brownian Motion

, 2011
In this paper, we consider a product of a symmetric stable process in $\mathbb{R}^d$ and a one-dimensional Brownian motion in $\mathbb{R}^+$. Then we define a class of harmonic functions with respect to this product process.
D Applebaum, Deniz Karlı, K-I Sato, L Grafakos, N Varopoulos, NV Krylov, PA Meyer, PA Meyer, PA Meyer, RF Bass, RF Bass   +10 more
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Harmonic functions with varying coefficients

Journal of Inequalities and Applications, 2016
Complex-valued harmonic functions that are univalent and sense preserving in the open unit disk can be written in the form f = h + g ‾ $f=h+\overline{g}$ , where h and g are analytic.
Jacek Dziok, Jay Jahangiri, Herb Silverman   +2 more
doaj   +1 more source