The Functional Calculus For Sectorial Operators PDF Download
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| Author | : Markus Haase |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 399 |
| Release | : 2006-08-18 |
| Genre | : Mathematics |
| ISBN | : 3764376988 |
Download The Functional Calculus for Sectorial Operators Book in PDF, ePub and Kindle
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 | : |
| Total Pages | : 221 |
| Release | : 2003 |
| Genre | : |
| ISBN | : |
Download The Functional Calculus for Sectorial Operators and Similarity Methods Book in PDF, ePub and Kindle
| Author | : Marcus Franciscus Uiterdijk |
| Publisher | : |
| Total Pages | : 24 |
| Release | : 1996 |
| Genre | : |
| ISBN | : |
Download A Note on the Functional Calculus for Sectorial Operators Book in PDF, ePub and Kindle
| Author | : Tamara Kucherenko |
| Publisher | : |
| Total Pages | : |
| Release | : 2005 |
| Genre | : Calculus |
| ISBN | : |
Download The Absolute Functional Calculus for Sectorial Operators Book in PDF, ePub and Kindle
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 | : Alexander Ullmann |
| Publisher | : |
| Total Pages | : |
| Release | : 2010 |
| Genre | : |
| ISBN | : |
Download Maximal Functions, Functional Calculus, and Generalized Triebel-Lizorkin Spaces for Sectorial Operators Book in PDF, ePub and Kindle
| Author | : Tuomas Hytönen |
| Publisher | : Springer |
| Total Pages | : 630 |
| Release | : 2018-02-14 |
| Genre | : Mathematics |
| ISBN | : 3319698087 |
Download Analysis in Banach Spaces Book in PDF, ePub and Kindle
This second volume of Analysis in Banach Spaces, Probabilistic Methods and Operator Theory, is the successor to Volume I, Martingales and Littlewood-Paley Theory. It presents a thorough study of the fundamental randomisation techniques and the operator-theoretic aspects of the theory. The first two chapters address the relevant classical background from the theory of Banach spaces, including notions like type, cotype, K-convexity and contraction principles. In turn, the next two chapters provide a detailed treatment of the theory of R-boundedness and Banach space valued square functions developed over the last 20 years. In the last chapter, this content is applied to develop the holomorphic functional calculus of sectorial and bi-sectorial operators in Banach spaces. Given its breadth of coverage, this book will be an invaluable reference to graduate students and researchers interested in functional analysis, harmonic analysis, spectral theory, stochastic analysis, and the operator-theoretic approach to deterministic and stochastic evolution equations.
| Author | : Stefan Gheorghe Juncu |
| Publisher | : |
| Total Pages | : 0 |
| Release | : 2015 |
| Genre | : |
| ISBN | : |
Download Functional Calculus with Applications to Tadmor-Ritt Operators Book in PDF, ePub and Kindle
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 | : F. Periago |
| Publisher | : |
| Total Pages | : 25 |
| Release | : 2000 |
| Genre | : Differential equations |
| ISBN | : |
Download A Functional Calculus for Non-sectorial Operators and Applications to Abstract Differential Equations Book in PDF, ePub and Kindle
| Author | : Markus Duelli |
| Publisher | : |
| Total Pages | : 0 |
| Release | : 2005 |
| Genre | : |
| ISBN | : 9783832508623 |
Download Functional Calculus for Bisectorial Operators and Applications to Linear and Non-linear Evolution Equations Book in PDF, ePub and Kindle
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 | : Carlos Bosch |
| Publisher | : World Scientific |
| Total Pages | : 226 |
| Release | : 2013 |
| Genre | : Mathematics |
| ISBN | : 9814415987 |
Download Functional Calculi Book in PDF, ePub and Kindle
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.
