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Refined Bohr-type inequalities with area measure for bounded analytic functions
Analysis and Mathematical Physics, 2020In this paper, we establish five new sharp versions of Bohr-type inequalities for bounded analytic functions in the unit disk by allowing Schwarz function in place of the initial coefficients in the power series representations of the functions involved ...
Yong Huang, Ming-Sheng Liu, S. Ponnusamy
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Exponential convergence of the deep neural network approximation for analytic functions
Science China Mathematics, 2018We prove that for analytic functions in low dimension, the convergence rate of the deep neural network approximation is exponential.
Weinan E, Qingcan Wang
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Composition Operators on Spaces of Analytic Functions
, 1995Introduction Analysis Background A Menagerie of Spaces Some Theorems on Integration Geometric Function Theory in the Disk Iteration of Functions in the Disk The Automorphisms of the Ball Julia-Caratheodory Theory in the Ball Norms Boundedness in ...
Helga Barbara Isselhard Mynott
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Complex Analysis, 2019
. For a function / analytic in the unit disc D, and for each X > 0, let L(X) = {z G D: |/(z)|= X) denote a level set for /. We introduce a class £, of functions characterized by geometric properties of a collection of sets (L(X„)}, where {X„} is an ...
J. S. Hwang, P. Lappan
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. For a function / analytic in the unit disc D, and for each X > 0, let L(X) = {z G D: |/(z)|= X) denote a level set for /. We introduce a class £, of functions characterized by geometric properties of a collection of sets (L(X„)}, where {X„} is an ...
J. S. Hwang, P. Lappan
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2011
In this lecture, we shall first prove Theorem 6.5 and then through simple examples demonstrate how easily this result can be used to check the analyticity of functions. We shall also show that the real and imaginary parts of an analytic function are solutions of the Laplace equation.
Sandra Pinelas +2 more
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In this lecture, we shall first prove Theorem 6.5 and then through simple examples demonstrate how easily this result can be used to check the analyticity of functions. We shall also show that the real and imaginary parts of an analytic function are solutions of the Laplace equation.
Sandra Pinelas +2 more
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Analytic structure on the spectrum of the algebra of symmetric analytic functions on $$L_\infty $$L∞
, 2020P. Galindo +2 more
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2009
In the previous chapter we discussed isotropic and anisotropic tensor functions and their general representations. Of particular interest in continuum mechanics are isotropic tensor-valued functions of one arbitrary (not necessarily symmetric) tensor. For example, the exponential function of the velocity gradient or other non-symmetric strain rates is ...
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In the previous chapter we discussed isotropic and anisotropic tensor functions and their general representations. Of particular interest in continuum mechanics are isotropic tensor-valued functions of one arbitrary (not necessarily symmetric) tensor. For example, the exponential function of the velocity gradient or other non-symmetric strain rates is ...
openaire +2 more sources