Results 11 to 20 of about 489,813 (268)
Algebraic formulas for the coefficients of mock theta functions and Weyl vectors of Borcherds products [PDF]
, 2017 We present some applications of the Kudla-Millson and the Millson theta lift. The two lifts map weakly holomorphic modular functions to vector valued harmonic Maass forms of weight $3/2$ and $1/2$, respectively.
Bruinier, Jan Hendrik +1 more
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Vector-valued holomorphic and harmonic functions
Concrete Operators, 2016 Holomorphic and harmonic functions with values in a Banach space are investigated. Following an approach given in a joint article with Nikolski [4] it is shown that for bounded functions with values in a Banach space it suffices that the composition with
Arendt Wolfgang
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Harmonic functions associated with Pascal distribution series
Scientific African, 2023 The primary objective of this paper is to explore the application of a specific convolution operator, which incorporates the Pascal distribution series. Through this investigation, we establish essential inclusion relations between the harmonic class HΥ ...
B.A. Frasin +3 more
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Multiply Harmonic Functions [PDF]
Nagoya Mathematical Journal, 1966 Let Ω and Ω′ be two locally compact, connected Hausdorff spaces having countable bases. On each of the spaces is defined a system of harmonic functions satisfying the axioms of M. Brelot [2]. The following is the description of such a system. To each open set of Ω is assigned a vector space of finite continuous functions, called the harmonic functions,
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COEFFICIENT CONDITIONS FOR HARMONIC CLOSE-TO-CONVEX FUNCTIONS [PDF]
, 2012 New sufficient conditions, concerned with the coefficients of harmonic functions $f(z)=h(z)+\bar{g(z)}$ in the open unit disk $\mathbb{U}$ normalized by $f(0)=h(0)=h'(0)-1=0$, for $f(z)$ to be harmonic close-to-convex functions are discussed. Furthermore,
HAYAMI, TOSHIO
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Fixed-energy harmonic functions
Discrete Analysis, 2017 Fixed-energy harmonic functions, Discrete Analysis 2017:18, 21 pp. The classical Dirichlet problem asks for a harmonic function in the interior of a region that takes specified values on the boundary.
Aaron Abrams, Richard Kenyon
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Harmonic functions on hyperbolic graphs [PDF]
, 2012 We consider admissible random walks on hyperbolic graphs. For a given harmonic function on such a graph, we prove that asymptotic properties of non-tangential boundedness and non-tangential convergence are almost everywhere equivalent.
Petit, Camille
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Some inequalities for strongly $(p,h)$-harmonic convex functions
Karpatsʹkì Matematičnì Publìkacìï, 2019 In this paper, we show that harmonic convex functions $f$ is strongly $(p, h)$-harmonic convex functions if and only if it can be decomposed as $g(x) = f(x) - c (\frac{1}{x^p})^2,$ where $g(x)$ is $(p, h)$-harmonic convex function.
M.A. Noor, K.I. Noor, S. Iftikhar
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Certain convex harmonic functions
International Journal of Mathematics and Mathematical Sciences, 2002 We define and investigate a family of complex-valued harmonic convex univalent functions related to uniformly convex analytic functions. We obtain coefficient bounds, extreme points, distortion theorems, convolution and convex combinations for this ...
Yong Chan Kim +2 more
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An extremal harmonic function [PDF]
Proceedings of the American Mathematical Society, 1969 surface 3x=h-'(X) and D(u; X) for the Dirichlet integral over the region ix bounded by a and fi. The main result of this paper is the inequality: maxhJ|Qx=m(h; X)=D(h; X)
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