The Cauchy formula with s-monogenic kernel and a functional calculus for noncommuting operators

By Fabrizio Colombo, Irene Sabadini. 2011

65 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/467e4e8e9f380618363ab5e0e96c0b821a376390

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In Algebra and Number Theory

In Applied Mathematics

Citations in the corpus

Slice regular functions on real alternative algebras (2010, methodology): “We define a Cauchy kernel, which in the quaternionic case was already introduced in [3], and for slice monogenic functions in [5, 6].”
Entire slice regular functions (2015, background): “The S-functional calculus, see [9, 45, 48, 49, 59, 60, 61, 71], is the analogue of the Riesz-Dunford functional calculus in the quaternionic setting.”
On Two Approaches to the Bergman Theory for Slice Regular Functions (2013, methodology): “In this paper we introduce the first elements and the settings of the Bergman theory in the case of slice regular functions studied in the papers [5–7, 9, 17].”
The $H^\infty$ functional calculus based on the $S$-spectrum for quaternionic operators and for $n$-tuples of noncommuting operators (2015, unknown): “, Tn) we can define the S-resolvent operators and the S-functional calculus, see [15, 18, 20].”
The Fueter mapping theorem in integral form and the ℱ‐functional calculus (2010, methodology): “Formula (1) is extremely good to define a functional calculus for n-tuples of non-necessarily commuting bounded or unbounded operators associated to slice monogenic functions f on suitable axially symmetric open sets as it was proved in [5].”
Pontryagin-de Branges-Rovnyak spaces of slice hyperholomorphic functions (2012, unknown): “[16, 18, 21]; while slice monogenic functions admit a functional calculus for n-tuples of operators, see [24, 20, 22].”
A New Resolvent Equation for the $$S$$S-Functional Calculus (2013, unknown): “, Tn) of non necessarily commuting operators and is based on the so-called S-spectrum, see [14, 17].”
Schur Functions and Their Realizations in the Slice Hyperholomorphic Setting (2011, background): “Slice monogenic functions admit a functional calculus for n-tuples of operators and for this theory we mention [43, 40, 36].”
An extension theorem for slice monogenic functions and some of its consequences (2010, background): “In a recent series of papers, [2], [ 3 ], [4] and [6], the authors have introduced and developed a new notion of monogenicity for Clifford algebra-valued functions defined on Euclidean spaces, which does not invoke the use of the Dirac operator, and in fact is defined in a completely independent fas”