Functions of the infinitesimal generator of a strongly continuous quaternionic group

DOI10.1142/S021953051650007XzbMath1370.47015arXiv1502.02954MaRDI QIDQ2962429

David P. Kimsey, Jonathan Gantner, Fabrizio Colombo, Daniel Alpay

Publication date: 16 February 2017

Published in: Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1502.02954

zbMATH Keywords

\(S\)-spectrumquaternionic functional calculus\(S\)-resolvent operatorfunctions of the infinitesimal generatorquaternionic infinitesimal generatorsquaternionic Laplace-Stieltjes transform

Mathematics Subject Classification ID

Functional calculus for linear operators (47A60) Spectrum, resolvent (47A10)

Related Items

On the equivalence of complex and quaternionic quantum mechanics ⋮ On power series expansions of the \(S\)-resolvent operator and the Taylor formula ⋮ Fractional powers of quaternionic operators and Kato’s formula using slice hyperholomorphicity ⋮ A Panorama on Quaternionic Spectral Theory and Related Functional Calculi ⋮ An Introduction to Fractional Powers of Quaternionic Operators and New Fractional Diffusion Processes ⋮ An application of the \(S\)-functional calculus to fractional diffusion processes ⋮ Fractional powers of vector operators and fractional Fourier’s law in a Hilbert space ⋮ The spectral theorem for quaternionic unbounded normal operators based on the S-spectrum ⋮ Quaternionic continuous wavelet transform on a quaternionic Hilbert space ⋮ Fractional powers of vector operators with first order boundary conditions ⋮ Perturbation of normal quaternionic operators ⋮ Operator Theory on One-Sided Quaternionic Linear Spaces: Intrinsic S-Functional Calculus and Spectral Operators ⋮ A simultaneous decomposition for three quaternion tensors with applications in color video signal processing ⋮ Schatten class and Berezin transform of quaternionic linear operators

Cites Work

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• The spectral theorem for unitary operators based on the \(S\)-spectrum
• Pontryagin-de Branges-Rovnyak spaces of slice hyperholomorphic functions
• Schur functions and their realizations in the slice hyperholomorphic setting
• Krein-Langer factorization and related topics in the slice hyperholomorphic setting
• A new resolvent equation for the \(S\)-functional calculus
• The quaternionic evolution operator
• Slice regular functions on real alternative algebras
• Noncommutative functional calculus. Theory and applications of slice hyperholomorphic functions
• Quaternion quantum mechanics: Second quantization and gauge fields
• On the formulations of the quaternionic functional calculus
• Topics in operator semigroups
• Semigroups of linear operators and applications to partial differential equations
• Quaternionic quantum field theory
• Schur functions, operator colligations, and reproducing kernel Pontryagin spaces
• The spectral theorem in quaternions
• On some properties of the quaternionic functional calculus
• A short course on operator semigroups
• Semigroups over real alternative *-algebras: Generation theorems and spherical sectorial operators
• The spectral theorem for quaternionic unbounded normal operators based on the S-spectrum
• CONTINUOUS SLICE FUNCTIONAL CALCULUS IN QUATERNIONIC HILBERT SPACES
• Regular Functions of a Quaternionic Variable
• Spectral Properties of Compact Normal Quaternionic Operators
• Spectral theory for unitary operators on a quaternionic Hilbert space
• Perturbation of the generator of a quaternionic evolution operator
• Normal Operators on Quaternionic Hilbert Spaces
• Analytic semigroups and optimal regularity in parabolic problems