Analysis of Dirac Systems and Computational Algebra

By Fabrizio Colombo, Irene Sabadini, F. Sommen, Daniele C. Struppa. 2004

311 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/d398dab67b230718de7c9337c054d28f00fc371d

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Citations in the corpus

Cauchy–Riemann Operators in Octonionic Analysis (2017, background): “[2]) hoping that the reader will get a better understanding of the octonionic analysis by comparing them to each other.”
On Some Properties of the Quaternionic Functional Calculus (2009, background): “We conclude by recalling that among the possible approaches to a functional calculus, there is one which makes use of functions with hypercomplex values and the function theory that plays an important role to treat the case of n-tuples of operators is the one of monogenic functions (see the classica”
Entire slice regular functions (2015, background): “It should be pointed out that the theory of slice hyperholomorphic functions is different from the more classical theory of functions in the kernel of the Dirac operator [35, 69, 84], the so-called monogenic functions.”
Schur Functions and Their Realizations in the Slice Hyperholomorphic Setting (2011, methodology): “We observe that another product in Clifford analysis (see [27, 42]), namely the CauchyKovaleskaya product which allows to obtain Cauchy-Fueter regular functions or monogenic functions, can be seen as a (different) convolution.”
A Cauchy kernel for slice regular functions (2009, background): “The classical, best known theory is the one due to Fueter [8,9] (see also [3] for recent developments).”
Extension results for slice regular functions of a quaternionic variable (2009, background): “The theory of slice regular functions is quite different from the more classical theory of regular functions in the sense of Cauchy–Fueter, see [9,10] and the more recent [6], and when compared with such theory, it shows many new and interesting features, such as the fact that it includes both polyn”
The $H^\infty$ functional calculus based on the $S$-spectrum for quaternionic operators and for $n$-tuples of noncommuting operators (2015, unknown): “Using a different approach, based on the classical theory of functions in the kernel of the Dirac operator, see [10, 19], A.”
A New Theory of Regular Functions of a Quaternionic Variable (2007, background): “While the theory is extremely successful in replicating many important properties of holomorphic functions (and not only in one variable, see [2]), the major disappointment is that even the identity f (q) = q , and therefore polynomials and series, fail to be regular in the sense of Fueter.”
Regular Moebius transformations of the space of quaternions (2008, background): “Recent work in the field includes [4] and references therein.”
The open mapping theorem for regular quaternionic functions (2008, background): “Recent work on this subject includes [1, 10] and references therein.”
The inverse Fueter mapping theorem (2011, methodology): “In the paper [9] the authors, using the Cauchy formula for slice monogenic functions, show an integral relation between monogenic functions, see [1], [8], [19], [23] and slice monogenic functions.”
A new functional calculus for noncommuting operators (2007, background): “The theory of such functions is fully developed in [1] (for the case of several Dirac operators see [3]), and the properties that such functions enjoy closely resemble those of holomorphic functions of a single complex variable.”
Zeros of regular functions and polynomials of a quaternionic variable (2008, background): “More recent work in this subject includes [1] and [9] and the references therein.”
Non Commutative Functional Calculus: Bounded Operators (2007, methodology): “For the complex case, the reader is referred to [5,6] and, by using the notion of monogenic functions with values in a Clifford algebra (see [7] for the case of one variable and [8] for the case of several variables), to [9] and the references therein.”