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Existence families, functional calculi, and evolution equations /

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This book presents an operator-theoretic approach to ill-posed evolution equations. It presents the basic theory, and the more surprising examples, of generalizations of strongly continuous semigroups known as 'existent families' and 'regularized semigroups'. These families of op...

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Bibliographic Details
Main Author: DeLaubenfels, Ralph, 1951-
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Berlin ; New York : Springer-Verlag, [1994]
Series:Lecture notes in mathematics (Springer-Verlag) ; 1570.
Subjects:
Evolution equations.
Linear operators.
Functional analysis.
Équations d'évolution.
Opérateurs linéaires.
Analyse fonctionnelle.
Lineaire operatoren.
Funktionalkalkül.
Evolutionsgleichung.
Cauchy-Anfangswertproblem.
Electronic books.
Online Access:Connect to the full text of this electronic book
Table of Contents:
  • I. Intuition and Elementary Examples
  • II. Existence Families
  • III. Regularized Semigroups
  • IV. The Solution Space of an Operator and Automatic Well-Posedness
  • V. Exponentially Bounded (Banach) Solution Space
  • VI. Well-posedness on a Larger Space; Generalized Solutions
  • VII. Entire Vectors and Entire Existence Families
  • VIII. Reversibility of Parabolic Problems
  • IX. The Cauchy Problem for the Laplace Equation
  • X. Boundary Values of Holomorphic Semigroups
  • XI. The Schrodinger Equation
  • XII. Functional Calculus for Commuting Generators of Bounded Strongly Continuous Groups
  • XIII. Petrovsky Correct Matrices of Generators of Bounded Strongly Continuous Groups
  • XIV. Arbitrary Matrices of Generators of Bounded Strongly Continuous Groups
  • XV. More Examples of Regularized Semigroups
  • XVI. Existence and Uniqueness Families
  • XVII. C-resolvents and Hille-Yosida Type Theorems
  • XVIII. Relationship to Integrated Semigroups
  • XIX. Perturbations
  • XX. Type of an Operator.
  • XXI. Holomorphic C-existence Families
  • XXII. Unbounded Holomorphic Functional Calculus for Operators with Polynomially Bounded Resolvents
  • XXIII. Spectral Conditions Guaranteeing Solutions of the Abstract Cauchy Problem
  • XXIV. Polynomials of Generators
  • XXV. Iterated Abstract Cauchy Problems
  • XXVI. Equipartition of Energy
  • XXVII. Simultaneous Solution Space
  • XXVIII. Exponentially Bounded Simultaneous Solution Space
  • XXIX. Simultaneous Existence Families
  • XXX. Simultaneous Existence Families for Matrices of Operators
  • XXXI. Time Dependent Evolution Equations.