The Cauchy-Kowalewski product for bicomplex holomorphic functions

DOI10.1002/mana.201100047zbMath1258.30023OpenAlexW2000190064MaRDI QIDQ2905239

Daniele C. Struppa, Hendrik De Bie, Adrian Vajiac, Mihaela Vajiac

Publication date: 27 August 2012

Published in: Mathematische Nachrichten (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/mana.201100047

zbMATH Keywords

Cauchy-Kowalewski extensionbicomplex numbersCauchy-Riemann systembiholomorphic functionsCRDGLS

Mathematics Subject Classification ID

Functions of hypercomplex variables and generalized variables (30G35) Cauchy-Kovalevskaya theorems (35A10)

Related Items (14)

Topological bicomplex modules ⋮ Bicomplex weighted Hardy spaces and bicomplex \(C^*\)-algebras ⋮ Complex Ternary Analysis and Applications ⋮ A new type of quaternionic regularity ⋮ An extension of the complex–real (C–R) calculus to the bicomplex setting, with applications ⋮ Some fundamental theorems of functional analysis with bicomplex and hyperbolic scalars ⋮ Interpolation with symmetry and a Herglotz theorem in the bicomplex setting ⋮ A note on the complex and bicomplex valued neural networks ⋮ Bicomplex neural networks with hypergeometric activation functions ⋮ Bicomplex Bergman and Bloch spaces ⋮ Bicomplex linear operators on bicomplex Hilbert spaces and Littlewood's subordination theorem ⋮ Bicomplex analogs of Segal-Bargmann and fractional Fourier transforms ⋮ Unnamed Item ⋮ Bicomplex holomorphic functional calculus

Cites Work

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• Special functions in Clifford analysis and axial symmetry
• Regular functions of several quaternionic variables and the Cauchy-Fueter complex
• Clifford-Hermite wavelets in Euclidean space
• Quaternionic hyperfunctions on five-dimensional varieties in \(\mathbb H^2\)
• Monogenic functions on surfaces.
• On a relation of bicomplex pseudoanalytic function theory to the complexified stationary Schrödinger equation
• NORMAL FAMILIES OF BICOMPLEX HOLOMORPHIC FUNCTIONS
• Complexified clifford analysis
• Sheaves of quaternionic hyperfunctions and microfunctions

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