scholarly journals Coefficients Characterization of Entire Harmonic Functions in Terms of Norm of Gradients at Origin in R^n, n≥ 3

2020 ◽  
Vol 13 (2) ◽  
pp. 258-268
Author(s):  
Devendra Kumar ◽  
Rajeev Kumar Vishnoi
Keyword(s):  
Harmonic Function ◽  
Lower Order ◽  
Spherical Harmonic ◽  
Harmonic Functions ◽  
Spherical Harmonic Expansion ◽  
Generalized Type ◽  
Generalized Order

Coefficient characterizations of generalized order, lower order and generalized type of entire harmonic function having the spherical harmonic expansion throughout a neighborhood of the origin in Rn have been obtained in terms of norm of gradients at origin.

scholarly journals On the generalized order and generalized type of entire monogenic functions

2013 ◽  
Vol 46 (4) ◽  
Author(s):  
G. S. Srivastava ◽  
Susheel Kumar
Keyword(s):  
Lower Order ◽  
Monogenic Functions ◽  
Generalized Type ◽  
Taylor’S Series ◽  
Generalized Order

AbstractIn the present paper we study the generalized growth of entire monogenic functions. The generalized order, generalized lower order and generalized type of entire monogenic functions have been obtained in terms of its Taylor’s series coefficients.

Generalized slow growth of special monogenic functions

2016 ◽  
Vol 22 (1) ◽  
Author(s):  
Susheel Kumar
Keyword(s):  
Taylor Series ◽  
Lower Order ◽  
Slow Growth ◽  
Monogenic Functions ◽  
Lower Type ◽  
Generalized Type ◽  
Generalized Order

AbstractIn the present paper we study the generalized slow growth of special monogenic functions. The characterizations of generalized order, generalized lower order, generalized type and generalized lower type of special monogenic functions have been obtained in terms of their Taylor series coefficients.

Growth and Approximation of Entire Harmonic Functions in 𝑅𝑛, 𝑛 > 3

2008 ◽  
Vol 15 (1) ◽  
pp. 99-110
Author(s):  
Devendra Kumar
Keyword(s):  
Harmonic Function ◽  
Spherical Harmonic ◽  
Harmonic Functions ◽  
Approximation Error

Abstract We study the growth of functions which are harmonic in any number of variables. The results are expressed in terms of spherical harmonic coefficients as well as by the approximation error of the harmonic function with (𝑝, 𝑞)-growth.

scholarly journals Generalized Growth of Special Monogenic Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Susheel Kumar
Keyword(s):  
Lower Order ◽  
Monogenic Functions ◽  
Lower Type ◽  
Generalized Type ◽  
Taylor’S Series ◽  
Generalized Order

We study the generalized growth of special monogenic functions. The characterizations of generalized order, generalized lower order, generalized type, and generalized lower type of special monogenic functions have been obtained in terms of their Taylor’s series coefficients.

Bergman-Harmonic Functions on Classical Domains

2019 ◽  
Author(s):  
Ming Xiao
Keyword(s):  
Harmonic Function ◽  
Future Study ◽  
Harmonic Functions ◽  
Boundary Regularity ◽  
Point Of View ◽  
Type I ◽  
Complex Manifolds ◽  
Classical Domain

Abstract We study Bergman-harmonic functions on classical domains from a new point of view in this paper. We first establish a boundary pluriharmonicity result for Bergman-harmonic functions on classical domains: a Bergman-harmonic function $u$ on a classical domain $D$ must be pluriharmonic on germs of complex manifolds in the boundary of $D$ if $u$ has some appropriate boundary regularity. Next we give a new characterization of pluriharmonicity on classical domains which may shed a new light on future study of Bergman-harmonic functions. We also prove characterization results for Bergman-harmonic functions on type I domains.

scholarly journals On the existence of various bounded harmonic functions with given periods, II

1975 ◽  
Vol 56 ◽  
pp. 1-5
Author(s):  
Masaru Hara
Keyword(s):  
Riemann Surface ◽  
Harmonic Function ◽  
Harmonic Functions ◽  
Dirichlet Integral ◽  
Period Function ◽  
Boundedness Property ◽  
One Dimensional ◽  
Bounded Harmonic Functions

Given a harmonic function u on a Riemann surface R, we define a period functionfor every one-dimensional cycle γ of the Riemann surface R. Γx(R) denote the totality of period functions Γu such that harmonic functions u satisfy a boundedness property X. As for X, we let B stand for boundedness, and D for the finiteness of the Dirichlet integral.

scholarly journals Harmonic Morphisms Projecting Harmonic Functions to Harmonic Functions

2012 ◽  
Vol 2012 ◽  
pp. 1-8
Author(s):  
M. T. Mustafa
Keyword(s):  
Harmonic Function ◽  
Riemannian Manifolds ◽  
Harmonic Functions ◽  
Horizontal Component ◽  
Harmonic Morphisms

For Riemannian manifoldsMandN, admitting a submersionϕwith compact fibres, we introduce the projection of a function via its decomposition into horizontal and vertical components. By comparing the Laplacians onMandN, we determine conditions under which a harmonic function onU=ϕ−1(V)⊂Mprojects down, via its horizontal component, to a harmonic function onV⊂N.

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