A survey on the recent advances in the spectral theory on the S-spectrum

DOI10.1007/978-3-031-21460-8_4OpenAlexW4364323271MaRDI QIDQ6160943

Fabrizio Colombo, David P. Kimsey

Publication date: 2 June 2023

Published in: Recent Developments in Operator Theory, Mathematical Physics and Complex Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-031-21460-8_4

zbMATH Keywords

universality propertyS-spectrumClifford spectral theoremmonogenic functions of a Clifford variable

Mathematics Subject Classification ID

Spectrum, resolvent (47A10) Quaternionic operator theory (47S05)

Cites Work

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• The spectral theorem for unitary operators based on the \(S\)-spectrum
• On the inversion of Fueter's theorem
• Slice hyperholomorphic Schur analysis
• The \(F\)-functional calculus for unbounded operators
• A new integral formula for the inverse Fueter mapping theorem
• A new resolvent equation for the \(S\)-functional calculus
• An extension theorem for slice monogenic functions and some of its consequences
• Slice regular functions on real alternative algebras
• Noncommutative functional calculus. Theory and applications of slice hyperholomorphic functions
• The inverse Fueter mapping theorem
• Fueter's theorem for monogenic functions in biaxial symmetric domains
• The Cauchy formula with s-monogenic kernel and a functional calculus for noncommuting operators
• Extension results for slice regular functions of a quaternionic variable
• The \(H^{\infty}\) functional calculus based on the \(S\)-spectrum for quaternionic operators and for \(n\)-tuples of noncommuting operators
• Slice monogenic functions
• A generalization of Fueter's theorem
• The Radon transform between monogenic and generalized slice monogenic functions
• On the formulations of the quaternionic functional calculus
• Holomorphic Cliffordian functions
• Clifford algebras, Fourier transforms and singular convolution operators on Lipschitz surfaces
• Generalization of Fueter's result to \(\mathbb{R}^{n+1}\)
• Singular integrals on star-shaped Lipschitz surfaces in the quaternionic space
• The spectral theorem in quaternions
• On the equivalence of complex and quaternionic quantum mechanics
• Spectral theory on the S-spectrum for quaternionic operators
• An application of the \(S\)-functional calculus to fractional diffusion processes
• Analysis of Dirac systems and computational algebra.
• Reproducing kernel quaternionic Pontryagin spaces
• Rational hyperholomorphic functions in \(\mathbb R^4\)
• Die Funktionentheorie der Differentialgleichungen \(\Delta u=0\) und \(\Delta\Delta u=0\) mit vier reellen Variablen
• Spectral properties of noncommuting operators
• Quaternionic analysis and elliptic boundary value problems
• The inverse Fueter mapping theorem in integral form using spherical monogenics
• The spectral theorem for normal operators on a Clifford module
• Universality property of the \(S\)-functional calculus, noncommuting matrix variables and Clifford operators
• The noncommutative fractional Fourier law in bounded and unbounded domains
• On some properties of the quaternionic functional calculus
• Fractional powers of vector operators with first order boundary conditions
• A new functional calculus for noncommuting operators
• A new theory of regular functions of a quaternionic variable
• An integral theorem for analytic intrinsic functions on quaternions
• The inverse Fueter mapping theorem for axially monogenic functions of degree \(k\)
• Semigroups over real alternative *-algebras: Generation theorems and spherical sectorial operators
• The spectral theorem for quaternionic unbounded normal operators based on the S-spectrum
• Application of Holomorphic Functions in Two and Higher Dimensions
• Formulations of the -functional calculus and some consequences
• Entire Slice Regular Functions
• The -spectrum and the -functional calculus
• Regular Functions of a Quaternionic Variable
• The Fueter mapping theorem in integral form and the ℱ-functional calculus
• Biaxial monogenic functions from Funk‐Hecke's formula combined with Fueter's theorem
• Fueter Mapping Theorem in Hypercomplex Analysis
• Duality theorems for slice hyperholomorphic functions
• The Weyl calculus and Clifford analysis
• Fractional powers of quaternionic operators and Kato’s formula using slice hyperholomorphicity
• Singular Integrals and Fourier Theory on Lipschitz Boundaries
• Quaternionic Approximation
• Fractional powers of vector operators and fractional Fourier’s law in a Hilbert space
• A nonconstant coefficients differential operator associated to slice monogenic functions
• Michele Sce's Works in Hypercomplex Analysis
• Slice monogenic functions of a Clifford variable via the 𝑆-functional calculus
• A Structure Formula for Slice Monogenic Functions and Some of its Consequences
• The structure of the fractional powers of the noncommutative Fourier law
• Quaternionic de Branges Spaces and Characteristic Operator Function
• Perturbation of normal quaternionic operators
• Quaternionic Closed Operators, Fractional Powers and Fractional Diffusion Processes
• Fractional powers of the noncommutative Fourier's law by the S‐spectrum approach
• Normal Operators on Quaternionic Hilbert Spaces

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