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Author: Markus Haase Publisher: Springer Science & Business Media ISBN: 3764376988 Category : Mathematics Languages : en Pages : 399
Book Description
This book contains a systematic and partly axiomatic treatment of the holomorphic functional calculus for unbounded sectorial operators. The account is generic so that it can be used to construct and interrelate holomorphic functional calculi for other types of unbounded operators. Particularly, an elegant unified approach to holomorphic semigroups is obtained. The last chapter describes applications to PDE, evolution equations and approximation theory as well as the connection with harmonic analysis.
Author: Markus Haase Publisher: Springer Science & Business Media ISBN: 3764376988 Category : Mathematics Languages : en Pages : 399
Book Description
This book contains a systematic and partly axiomatic treatment of the holomorphic functional calculus for unbounded sectorial operators. The account is generic so that it can be used to construct and interrelate holomorphic functional calculi for other types of unbounded operators. Particularly, an elegant unified approach to holomorphic semigroups is obtained. The last chapter describes applications to PDE, evolution equations and approximation theory as well as the connection with harmonic analysis.
Author: Tamara Kucherenko Publisher: ISBN: Category : Calculus Languages : en Pages :
Book Description
We introduce the absolute functional calculus for sectorial operators. This notion is stronger than the common holomorphic functional calculus. We are able to improve a key theorem related to the maximal regularity problem and hence demonstrate the power and usefulness of our new concept. In trying to characterize spaces where sectorial operators have absolute calculus, we find that certain real interpolation spaces play a central role. We are then extending various known results in this setting. The idea of unifying theorems about sectorial operators on real interpolation spaces permeates our work and opens paths for future research on this subject.
Author: Markus Duelli Publisher: ISBN: 9783832508623 Category : Languages : en Pages : 0
Book Description
The holomorphic functional calculus for sectorial unbounded operators is an extension of the classical Dunford calculus for bounded operators. The interest in this calculus is motivated by the Kato square root problem and applications to the operator-sum method introduced by DaPrato and Grisvard to treat evolution equations on a finite interval. In this thesis we develop the holomorphic functional calculus for multisectorial and asymptotically bisectorial operators. We obtain versions of closed-sum theorems that allow to deduce maximal regularity for first and second order Cauchy problems both on the line and for the periodic problem. The results are then applied to prove existence and uniqueness of non-linear evolution equations.
Author: Stefan Gheorghe Juncu Publisher: ISBN: Category : Languages : en Pages : 0
Book Description
One can give various rigorous definitions to the notion of "functional calculus", but a functional calculus is ultimately just a mathematically meaningful way of talking about an operator f(T), where, T is an operator and f is a function. This thesis is concerned with this concept and with one of its applications, the finding of bounds for powers of operators. It is actually this very application that has prompted the entire investigation presented here. This application is relevant to various fields, such as the numerical analysis of PDE and Markov chains. Chapter I presents various abstract approaches to the notion of "functional calculus" that are given content by three major examples: the Riesz-Dunford functional calculus, the Weyl functional calculus and the functional calculus for sectorial operators. Chapter II investigates various conditions that ensure power boundedness for operators, putting the Tadmor-Ritt condition at its center. The Riesz-Dunford calculus is instrumental for the proofs in this chapter. Chapter III investigates Pascale Vitse's use of Cauchy-Stieltjes integrals and their multipliers for obtaining bounds on powers of operators; the chapter closes with an investigation of partially power bounded operators.
Author: Carlos Bosch Publisher: World Scientific ISBN: 9814415987 Category : Mathematics Languages : en Pages : 226
Book Description
A functional calculus is a construction which associates with an operator or a family of operators a homomorphism from a function space into a subspace of continuous linear operators, i.e. a method for defining OC functions of an operatorOCO. Perhaps the most familiar example is based on the spectral theorem for bounded self-adjoint operators on a complex Hilbert space.This book contains an exposition of several such functional calculi. In particular, there is an exposition based on the spectral theorem for bounded, self-adjoint operators, an extension to the case of several commuting self-adjoint operators and an extension to normal operators. The Riesz operational calculus based on the Cauchy integral theorem from complex analysis is also described. Finally, an exposition of a functional calculus due to H. Weyl is given.
Author: Giuseppe Da Prato Publisher: Springer ISBN: 3540446532 Category : Mathematics Languages : en Pages : 478
Book Description
This book consists of five introductory contributions by leading mathematicians on the functional analytic treatment of evolutions equations. In particular the contributions deal with Markov semigroups, maximal L^p-regularity, optimal control problems for boundary and point control systems, parabolic moving boundary problems and parabolic nonautonomous evolution equations. The book is addressed to PhD students, young researchers and mathematicians doing research in one of the above topics.
Author: Markus Haase
Author: Markus Haase
Author: Marcus Franciscus Uiterdijk
Author: Markus Haase
Author: Tamara Kucherenko
Author: Markus Duelli
Author: Alexander Ullmann
Author: Stefan Gheorghe Juncu
Author: Carlos Bosch
Author: F. Periago
Author: Giuseppe Da Prato