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Existence families, functional calculi, and evolution equations

Author: Ralph DeLaubenfels
Publisher: Berlin ; New York : Springer-Verlag, ©1994.
Series: Lecture notes in mathematics (Springer-Verlag), 1570.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:

One thinks of a semigroup generated by A as etA and thinks of a regularized semigroup generated by A as etA g(A), producing solutions of the abstract Cauchy problem for initial data in the image of  Read more...

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Additional Physical Format: Online version:
DeLaubenfels, Ralph, 1951-
Existence families, functional calculi, and evolution equations.
Berlin ; New York : Springer-Verlag, ©1994
(OCoLC)624506149
Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Ralph DeLaubenfels
ISBN: 0387577033 9780387577036 3540577033 9783540577034
OCLC Number: 29595385
Description: xv, 234 pages ; 24 cm.
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.
Series Title: Lecture notes in mathematics (Springer-Verlag), 1570.
Responsibility: Ralph deLaubenfels.

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