Zobrazeno 1 - 10
of 147
pro vyhledávání: '"Perotti, Alessandro"'
We provide a classification of Fueter-regular quaternionic functions $f$ in terms of the degree of complex linearity of their real differentials $df$. Quaternionic imaginary units define orthogonal almost-complex structures on the tangent bundle of t
Externí odkaz:
http://arxiv.org/abs/2411.00127
Autor:
Perotti, Alessandro
We introduce Wirtinger operators for functions of several quaternionic variables. These operators are real linear partial differential operators which behave well on quaternionic polynomials, with properties analogous to the ones satisfied by the Wir
Externí odkaz:
http://arxiv.org/abs/2212.10868
Autor:
Perotti, Alessandro
Publikováno v:
Journal of Mathematical Analysis and Applications, 516 (2022) 126480
We prove some formulas relating Cauchy-Riemann operators defined on hypercomplex subspaces of an alternative *-algebra to a differential operator associated with the concept of slice-regularity and to the spherical Dirac operator. These results in pa
Externí odkaz:
http://arxiv.org/abs/2201.09981
Publikováno v:
J. Noncommut. Geom., 16(2): 637--676 (2022)
This work looks at the theory of octonionic slice regular functions through the lens of differential topology. It proves a full-fledged version of the Open Mapping Theorem for octonionic slice regular functions. Moreover, it opens the path for a poss
Externí odkaz:
http://arxiv.org/abs/2109.12902
Autor:
Perotti, Alessandro
Publikováno v:
Computational Methods and Function Theory (2023)
We prove a Cauchy-type integral formula for slice-regular functions where the integration is performed on the boundary of an open subset of the quaternionic space, with no requirement of axial symmetry. In particular, we get a local Cauchy-type integ
Externí odkaz:
http://arxiv.org/abs/2105.07041
Publikováno v:
Ann. Mat. Pura e Appl., 201:2519-2548 (2022)
This paper addresses particular eigenvalue problems within the context of two quaternionic function theories. More precisely, we study two concrete classes of quaternionic eigenvalue problems, the first one for the slice derivative operator in the cl
Externí odkaz:
http://arxiv.org/abs/2103.14868
Autor:
Ghiloni, Riccardo, Perotti, Alessandro
Publikováno v:
Mathematische Zeitschrift 302(1):295-351 (2022)
In this paper, we lay the foundations of the theory of slice regular functions in several variables ranging in any real alternative $^*$-algebra, including quaternions, octonions and Clifford algebras. This theory is an extension of the classical the
Externí odkaz:
http://arxiv.org/abs/2007.14925
Autor:
Perotti, Alessandro
Publikováno v:
Complex Variables and Elliptic Equations, 66:8, 1287-1297 (2021)
We present an Almansi-type decomposition for polynomials with Clifford coefficients, and more generally for slice-regular functions on Clifford algebras. The classical result by Emilio Almansi, published in 1899, dealt with polyharmonic functions, th
Externí odkaz:
http://arxiv.org/abs/2004.06535
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