Spectral Properties of Noncommuting Operators

By B. Jefferies. 2004

104 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/5f5a56c72b2e7460226077c18f8fa48eaf3330bd

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Citations in the corpus

Bicomplex holomorphic functional calculus (2014, background): “which is the a natural extension of the holomorphic functional calculus to quaternionic operators and to n-tuples of noncommuting operators (see the book [4]), and the monogenic functional calculus based on the classical theory of monogenic functions (see the book [8]).”
Entire slice regular functions (2015, background): “The F-functional calculus, see [18, 41, 63, 67, 68], which is based on the Fueter mapping theorem in integral form, is a monogenic functional calculus in the spirit of the one developed in [128, 129, 130, 138, 134], but it is associated to slice hyperholomorphicity.”
The Fueter mapping theorem in integral form and the ℱ‐functional calculus (2010, methodology): “The functional calculus we construct is inspired by the functional calculus introduced, for example, in [23].”
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.”
The $H^\infty$ functional calculus based on the $S$-spectrum for quaternionic operators and for $n$-tuples of noncommuting operators (2015, unknown): “McIntosh with some of his coauthors developed the monogenic functional calculus, see [32, 33, 34, 35, 36], and based on it he also developed the H∞ functional calculus for commuting operators see [29].”
On Some Properties of the Quaternionic Functional Calculus (2009, result): “Since the literature in this setting is very wide we mention, without claim of completeness, the papers [14–17, 19, 21, 22] and the literature therein.”
A new functional calculus for noncommuting operators (2007, methodology): “If we formally replace zj by Tj in the Cauchy kernel series, it can be shown (see [5], Lemma 4.”
A Structure Formula for Slice Monogenic Functions and Some of its Consequences (2008, background): “We mention here, without claim completeness, the works [7], [8], [9], [10], [11] and the literature therein.”
A New Resolvent Equation for the $$S$$S-Functional Calculus (2013, unknown): “Jefferies and their coauthors (see [27, 28, 30, 33], the monograph [26] and the references therein) who first used the theory of hyperholomorphic functions, see [10, 18, 20, 25], to define a hyperholomorphic functional calculus for n-tuples of operators.”