A Panorama on Quaternionic Spectral Theory and Related Functional Calculi

DOI10.1007/978-3-319-42529-0_6zbMath1388.30068OpenAlexW2554935616MaRDI QIDQ4637344

Publication date: 18 April 2018

Published in: Trends in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-319-42529-0_6

zbMATH Keywords

\(S\)-functional calculus \(H^\infty\)-functional calculus \(F\)-functional calculus \(W\)-functional calculus Philips functional calculus quaternionic spectral theory

Mathematics Subject Classification ID

Functions of hypercomplex variables and generalized variables (30G35) Research exposition (monographs, survey articles) pertaining to functions of a complex variable (30-02)

Cites Work

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The spectral theorem for unitary operators based on the \(S\)-spectrum
On power series expansions of the \(S\)-resolvent operator and the Taylor formula
Slice hyperholomorphic Schur analysis
An extension of Herglotz's theorem to the quaternions
The \(F\)-functional calculus for unbounded operators
A new resolvent equation for the \(S\)-functional calculus
The quaternionic evolution operator
Noncommutative functional calculus. Theory and applications of slice hyperholomorphic functions
The \(H^{\infty}\) functional calculus based on the \(S\)-spectrum for quaternionic operators and for \(n\)-tuples of noncommuting operators
Quaternion quantum mechanics: Second quantization and gauge fields
On the formulations of the quaternionic functional calculus
Quaternionic quantum field theory
Generalization of Fueter's result to \(\mathbb{R}^{n+1}\)
The spectral theorem in quaternions
Spectral properties of noncommuting operators
On some properties of the quaternionic functional calculus
Matrices of quaternions
Monogenic plane waves and the W -functional calculus
Semigroups over real alternative *-algebras: Generation theorems and spherical sectorial operators
The spectral theorem for quaternionic unbounded normal operators based on the S-spectrum
Formulations of the -functional calculus and some consequences
CONTINUOUS SLICE FUNCTIONAL CALCULUS IN QUATERNIONIC HILBERT SPACES
Regular Functions of a Quaternionic Variable
Spectral Properties of Compact Normal Quaternionic Operators
Functions of the infinitesimal generator of a strongly continuous quaternionic group
Spectral theory for unitary operators on a quaternionic Hilbert space
The Fueter mapping theorem in integral form and the ℱ-functional calculus
The Weyl calculus and Clifford analysis
Fractional powers of quaternionic operators and Kato’s formula using slice hyperholomorphicity
A Structure Formula for Slice Monogenic Functions and Some of its Consequences
Perturbation of the generator of a quaternionic evolution operator
Normal Operators on Quaternionic Hilbert Spaces
Quaternions and matrices of quaternions

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