Search Results - holomorphic functions of several hypercomplex variables

Construction of solutions to PDEs using holomorphic functions of several variables by Shpakivskyi, Vitalii

“…  Laplace, Helmholtz, and Poisson equations in the form of components  of holomorphic functions of several variables…”
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On the Rate of Polynomial Approximations of Holomorphic Functions on Convex Compact Sets by Smirnov, Matvey

“…We prove that a holomorphic function on a neighborhood of a compact convex set K…”
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Slice regular functions in several variables by Ghiloni, Riccardo, Perotti, Alessandro

“… This higher dimensional function theory is an extension of the classical theory of holomorphic functions of several complex variables…”
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O-Regular Mappings on C(C): A Structured Operator–Theoretic Framework by Kim, Ji Eun

“… While Dirac-type frameworks are classical in several complex variables and Clifford analysis, a coherent calculus aligning structural CR systems, a canonical first derivative, and a Cauchy-type…”
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Characterizations of Herglotz–Nevanlinna Functions Using Positive Semi-Definite Functions and the Nevanlinna Kernel in Several Variables by Nedic, Mitja

“… This allows us to propose a multidimensional analogue of the classical Nevanlinna kernel and a definition of generalized Nevanlinna functions in several variables…”
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Laguerre derivative and monogenic Laguerre polynomials: An operational approach by Cação, I., Falcão, M.I., Malonek, H.R.

“…Hypercomplex function theory generalizes the theory of holomorphic functions of one complex variable by using Clifford Algebras and provides the fundamentals of Clifford Analysis as a refinement…”
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Weak Slice Regular Functions on the n-Dimensional Quadratic Cone of Octonions by Dou, Xinyuan, Ren, Guangbin, Sabadini, Irene, Yang, Ting

“…), the second one makes use of stem and slice functions. So far, in the setting of several hypercomplex variables, only the second approach has been considered, i.e…”
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Some Properties of the Slice Regular Schwarzians by Oscar, González-Cervantes J

“…The complex Schwarzian is a complex differential operator with several applications and properties in the theory of functions of one complex variable, such as the…”
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Regular Moebius transformations of the space of quaternions by Stoppato, Caterina

“… Several properties of regular quaternionic functions are analogous to those of holomorphic functions of one complex variable, although the diversity of the non-commutative setting introduces new phenomena…”
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The Corona Problem, Carleson Measures, and Applications by Saracco, Alberto

“…Carleson measures were introduced by Lennart Carleson in 1962 to solve an interpolation problem about bounded holomorphic function called the corona problem…”
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The Cauchy Integral Formula in Hermitian, Quaternionic and osp(4|2) Clifford Analysis by Brackx, F., De Schepper, H., Lávička, R., Souček, V.

“…As is the case for the theory of holomorphic functions in the complex plane, the Cauchy Integral Formula has proven to be a cornerstone of Clifford analysis, the monogenic function theory in higher…”
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Weak slice regular functions on the \(n\)-dimensional quadratic cone of octonions by Dou, Xinyuan, Ren, Guangbin, Sabadini, Irene, Yang, Ting

“…), the second one makes use of stem and slice functions. So far, in the setting of several hypercomplex variables, only the second approach has been considered, i.e…”
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