Existence Families, Functional Calculi and Evolution Equations

Häftad, Engelska, 1994

Del 1570 i serien Lecture Notes in Mathematics

488 kr

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Beskrivning

This monograph 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 operators may be used either to produce all initial data for which a solution in the original space exists, or to construct a maximal subspace on which the problem is well-posed. Regularized semigroups are also used to construct functional, or operational, calculi for unbounded operators.

Produktinformation

Utgivningsdatum:1994-03-28
Mått:155 x 235 x 15 mm
Vikt:400 g
Format:Häftad
Språk:Engelska
Serie:Lecture Notes in Mathematics
Antal sidor:244
Upplaga:1994
Förlag:Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
ISBN:9783540577034

Utforska kategorier

Innehållsförteckning

Intuition and elementary examples.- Existence families.- Regularized semigroups.- The solution space of an operator and automatic well-posedness.- Exponentially bounded (Banach) solution spaces.- Well-posedness on a larger space; Generalized solutions.- Entire vectors and entire existence families.- Reversibility of parabolic problems.- The cauchy problem for the Laplace equation.- Boundary values of holomorphic semigroups.- The Schrödinger equation.- Functional calculus for commuting generators of bounded strongly continuous groups.- Petrovsky correct matrices of generators of bounded strongly continuous groups.- Arbitrary matrices of generators of bounded strongly continuous groups.- More examples of regularized semigroups.- Existence and uniqueness families.- C-resolvents and Hille-Yosida type theorems.- Relationship to integrated semigroups.- Perturbations.- Type of an operator.- Holomorphic C-existence families.- Unbounded holomorphic functional calculus for operators with polynomially bounded resolvents.- Spectral conditions guaranteeing solutions of the abstract Cauchy problem.- Polynomials of generators.- Iterated abstract Cauchy problems.- Equipartition of energy.- Simultaneous solution space.- Exponentially bounded simultaneous solution space.- Simultaneous existence families.- Simultaneous existence families for matrices of operators.- Time dependent evolution equations.