An application of the \(S\)-functional calculus to fractional diffusion processes

DOI10.1007/s00032-018-0287-zzbMath1447.47063arXiv1803.10528OpenAlexW2963110883WikidataQ129100766 ScholiaQ129100766MaRDI QIDQ1756609

Jonathan Gantner, Fabrizio Colombo

Publication date: 21 December 2018

Published in: Milan Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1803.10528

zbMATH Keywords

\(S\)-spectrum\(H^\infty\) functional calculus for quaternionic operatorsfractional diffusion and fractional evolution processesfractional powers of vector operators

Mathematics Subject Classification ID

Fractional derivatives and integrals (26A33) Functional calculus for linear operators (47A60) Spectrum, resolvent (47A10) Diffusion processes (60J60) Applications of operator theory to differential and integral equations (47N20) Quaternionic operator theory (47S05)

Related Items (14)

Time-space fractional diffusion problems: existence, decay estimates and blow-up of solutions ⋮ Harmonic and polyanalytic functional calculi on the \(S\)-spectrum for unbounded operators ⋮ A survey on the recent advances in the spectral theory on the S-spectrum ⋮ Quaternionic triangular linear operators ⋮ Infinite-order differential operators acting on entire hyperholomorphic functions ⋮ The noncommutative fractional Fourier law in bounded and unbounded domains ⋮ Fractional powers of vector operators and fractional Fourier’s law in a Hilbert space ⋮ An introduction to hyperholomorphic spectral theories and fractional powers of vector operators ⋮ 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 ⋮ Axially harmonic functions and the harmonic functional calculus on the \(S\)-spectrum ⋮ Universality property of the \(S\)-functional calculus, noncommuting matrix variables and Clifford operators ⋮ Fractional powers of higher-order vector operators on bounded and unbounded domains

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