Noncommutative Functional Calculus

By Fabrizio Colombo, Irene Sabadini, Daniele C. Struppa. 2011

336 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/5c15af269fa5d3a4afc890a3978832a56658522f

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In Applied Mathematics

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Citations in the corpus

The inverse Fueter mapping theorem (2011, background): “Its main importance is that it allows a natural definition of a functional calculus for n-tuples of non necessarily commuting operators, see [6] and [12] and the book [14] in which it is also developed the theory of the quaternionic functional calculus see also [7].”
The Fock Space in the Slice Hyperholomorphic Setting (2014, methodology): “One of the applications of the Representation Formula is the fact that any function defined on an open set ΩI of a complex plane CI which belongs to the kernel of the Cauchy-Riemann operator can be uniquely extended to a slice hyperholomorphic function defined on the axially symmetric completion of ”
The algebra of slice functions (2015, background): “The basic material on slice monogenicity is collected in [6], which also points out the original references.”
The C-property for slice regular functions and applications to the Bergman space (2013, background): “After their definition in [2], which has been generalized to the case of functions with values in a Clifford algebra in [3], these functions have been intensively studied during the past years and their theory, as well as the application to the functional calculus, is treated in [4].”
Bicomplex holomorphic functional calculus (2014, background): “Also for quaternionic, bounded linear operators (where the notion of spectrum has to be substituted by the notion of S-spectrum), we have that the S-spectrum is compact and non empty see [4].”
The spectral theorem for quaternionic unbounded normal operators based on the S-spectrum (2014, background): “We recall some properties, see [16], of the S-spectrum.”
The $H^\infty$ functional calculus based on the $S$-spectrum for quaternionic operators and for $n$-tuples of noncommuting operators (2015, neutral): “The case of n-tuples of operators The notion of slice hyperholomorphicity can be given for Clifford algebra-valued functions, see [20].”
The Spectral Theorem for Unitary Operators Based on the S-Spectrum (2014, positive): “We will be in need of the Cauchy formula for slice hyperholomorphic functions, see [17] for more details.”
A nonconstant coefficients differential operator associated to slice monogenic functions (2012, background): “In the past few years, the theory of slice monogenic functions has had a rapid development mainly stimulated by the application to a very elegant functional calculus for not necessarily commuting operators, either bounded or unbounded; see [2, 4, 7, 8, 9] and the recent monograph [10].”
A New Resolvent Equation for the $$S$$S-Functional Calculus (2013, neutral): “For more details on the S-functional calculus and the function theory on which it is based see the the monograph [19].”
Entire slice regular functions (2015, methodology): “[23, 76, 108], we repeated them to make the monograph self-contained.”
Pontryagin-de Branges-Rovnyak spaces of slice hyperholomorphic functions (2012, positive): “In this paper, we consider a notion which includes power series in the quaternionic variable, the so-called slice regular or slice hyperholomorphic functions; see [33].”