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Author Colombo, Fabrizio, author
Title Quaternionic closed operators, fractional powers and fractional diffusion processes / Fabrizio Colombo, Jonathan Gantner
Imprint Cham, Switzerland : Birkhauser/Springer Nature Switzerland AG, [2019]
book jacket
 Mathematics Library  QA329.2 C65 2019    AVAILABLE    30340200563694
Descript viii, 322 pages ; 25 cm
text txt rdacontent
unmediated n rdamedia
volume nc rdacarrier
Series Operator theory: Advances and applications, 0255-0156 ; Volume 274
Operator theory, advances and applications ; v. 274
Note Includes bibliographical references (pages 307-320) and index
Also available online
Current copyright fee: GBP34.00 22\1. Uk
Introduction -- Theoretical aspects -- Applications to fractional diffusion processes -- On quaternionic spectral theories -- Preliminary results -- Slice hyperholomorphic functions -- The S-functional calculus for bounded operators -- Bounded operators with commuting components -- The direct approach to the S-functional calculus -- Properties of the S-spectrum of a closed operator -- The S-resolvent of a closed operator -- Closed operators with commuting components -- The S-functional calculus and its properties -- The product rule and polynomials in T -- The spectral mapping theorem -- Spectral sets and projections onto invariant subspaces -- The special roles of intrinsic functions and the left multiplication -- The Quaternionic Evolution Operator -- Uniformly continuous quaternionic semigroups -- Strongly continuous quaternionic semigroups -- Strongly continuous groups -- Perturbations of the generator of a group -- A series expansion of the S-resolvent operator -- The class of operators A(T) and some properties -- Perturbation of the generator -- Comparison with the complex setting -- An application -- The Phillips functional calculus -- Preliminaries on quaternionic measure theory -- Functions of the generator of a strongly continuous group -- Comparison with the S-Functional Calculus -- The Inversion of the Operator f(T) -- The ... -Functional Calculus -- The S-functional calculus for sectorial operators -- The ... -functional calculus -- The composition rule -- Extensions according to spectral conditions -- The spectral mapping theorem -- Fractional powers of quaternionic linear operators -- A direct approach to fractional powers of negative exponent -- Fractional powers via the ... -functional calculus -- Fractional powers with negative real part -- Kato's Formula for the S-Resolvents -- The fractional heat equation using quaternionic techniques -- Spectral properties of the Nabla operator -- A relation with the fractional heat equation -- An example with non-constant coefficients -- Applications to fractional diffusion -- New fractional diffusion problems -- The S-spectrum approach to fractional diffusion processes -- Fractional Fourier's law in a Hilbert space -- Concluding Remarks -- Historical notes and References -- Theory of slice hyperholomorphic functions -- Spectral theory on the S-spectrum -- The monographs on operators and functions -- Appendix : Principles of functional Analysis -- Bibliography -- Index
Subject Closed operators
Fractional powers
Alt Author Gantner, Jonathan, author
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