On the relation between the growth and the Taylor coefficients of entire solutions to the higher-dimensional Cauchy--Riemann system in \(\mathbb R^{n+1}\)

DOI10.1016/J.JMAA.2006.04.055zbMath1108.30041OpenAlexW2089182852MaRDI QIDQ860612

R. De Almeida, Denis Constales, Rolf Sören Krausshar

Publication date: 9 January 2007

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2006.04.055

zbMATH Keywords

Clifford analysismaximum modulusgeneralized trigonometric functionsentire holomorphic functionsgrowth orders

Mathematics Subject Classification ID

Functions of hypercomplex variables and generalized variables (30G35) Special classes of entire functions of one complex variable and growth estimates (30D15)

Related Items (20)

Generalized slow growth of special monogenic functions ⋮ Generalized growth orders for polymonogenic functions and related inequalities ⋮ Basics on growth orders of polymonogenic functions ⋮ On the lower order and type of entire axially monogenic functions ⋮ Some remarks on the generalized order and generalized type of entire functions of several complex matrices ⋮ Entire monogenic functions of given proximate order and continuous homomorphisms ⋮ On Hadamard's three‐hyperballs theorem and its applications to Whittaker‐Cannon hypercomplex theory ⋮ Wiman-Valiron theory for the Dirac-Hodge equation on upper half-space of \(\mathbb R^{n+1}\) ⋮ Unnamed Item ⋮ Generalized growth of monogenic Taylor series of finite convergence radius ⋮ Infinite-order differential operators acting on entire hyperholomorphic functions ⋮ On the generalized order and generalized type of entire monogenic functions ⋮ Bernoulli special monogenic polynomials with the difference and sum polynomial bases ⋮ Basics of a generalized Wiman-Valiron theory for monogenic Taylor series of finite convergence radius ⋮ Lower growth of generalized Hadamard product functions in Clifford setting ⋮ On the growth order and growth type of entire functions of several complex matrices ⋮ A note on the growth order of the inverse and product bases of special monogenic polynomials ⋮ Unnamed Item ⋮ Generalized growth of special monogenic functions ⋮ Bernoulli and Euler polynomials in Clifford analysis

Cites Work

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• On the order of basic series representing Clifford valued functions.
• Order theory for isolated points of monogenic functions
• On the convergence properties of basic series representing special monogenic functions
• Representation formulas for the general derivatives of the fundamental solution to the Cauchy-Riemann operator in Clifford analysis and applications
• On the asymptotic growth of entire monogenic functions
• Basic sets of pofynomials in clifford analysis
• The Local Growth of Power Series: A Survey of the Wiman-Valiron Method
• On the lower order of integral functions

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