Weak Slice Regular Functions on the n-Dimensional Quadratic Cone of Octonions
Copyright policy )Weak Slice Regular Functions on the n-Dimensional Quadratic Cone of Octonions
AbstractIn the literature on slice analysis in the hypercomplex setting, there are two main approaches to define slice regular functions in one variable: one consists in requiring that the restriction to any complex plane is holomorphic (with the same complex structure of the complex plane), 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. the one based on stem functions. In this paper, we use instead the first definition on the so-called n-dimensional quadratic cone of octonions. These two approaches yield the same class of slice regular functions on axially symmetric slice-domains, however, they are different on other types of domains. We call this new class of functions weak slice regular. We show that there exist weak slice regular functions which are not slice regular in the second approach. Moreover, we study various properties of these functions, including a Taylor expansion.
- University of Science and Technology of China China (People's Republic of)
- Nanjing Normal University China (People's Republic of)
- Anqing Normal University China (People's Republic of)
- Anyang Normal University China (People's Republic of)
- Daqing Normal University China (People's Republic of)
Artificial intelligence, Class (philosophy), Octonions, Holomorphic functions of several complex variables, functions of hypercomplex variable, Geometry, Complex plane, Evolutionary biology, representation formula, Holomorphic function, Plane (geometry), Mathematical analysis, slice regular functions, Functions of hypercomplex variables and generalized variables, Taylor series, FOS: Mathematics, Complex Variables (math.CV), Optoelectronics, Variable (mathematics), Hypercomplex number, Biology, Functions of hypercomplex variable, Algebra over a field, Representation formula, Mathematics - Complex Variables, Applied Mathematics, Wafer, Physics, Fractional Fourier Transform Analysis, Symplectic Topology and Knot Invariants, Pure mathematics, Quadratic equation, Cone (formal languages), Discrete mathematics, Computer science, Quaternionic Analysis and Applications, 30G35 (Primary), 32A10 (Secondary), Algorithm, Quaternion, octonions, Slice Regular Functions, Function (biology), Physical Sciences, Geometry and Topology, Slice regular functions, Mathematics
Artificial intelligence, Class (philosophy), Octonions, Holomorphic functions of several complex variables, functions of hypercomplex variable, Geometry, Complex plane, Evolutionary biology, representation formula, Holomorphic function, Plane (geometry), Mathematical analysis, slice regular functions, Functions of hypercomplex variables and generalized variables, Taylor series, FOS: Mathematics, Complex Variables (math.CV), Optoelectronics, Variable (mathematics), Hypercomplex number, Biology, Functions of hypercomplex variable, Algebra over a field, Representation formula, Mathematics - Complex Variables, Applied Mathematics, Wafer, Physics, Fractional Fourier Transform Analysis, Symplectic Topology and Knot Invariants, Pure mathematics, Quadratic equation, Cone (formal languages), Discrete mathematics, Computer science, Quaternionic Analysis and Applications, 30G35 (Primary), 32A10 (Secondary), Algorithm, Quaternion, octonions, Slice Regular Functions, Function (biology), Physical Sciences, Geometry and Topology, Slice regular functions, Mathematics
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