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Mathematical Foundations of the State Lumping of Large Systems by Vladimir S. Ko
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Item specifics
- Condition
- Brand New: A new, unread, unused book in perfect condition with no missing or damaged pages. See all condition definitionsopens in a new window or tab
- ISBN-13
- 9780792324133
- Book Title
- Mathematical Foundations of the State Lumping of Large Systems
- ISBN
- 9780792324133
- Publication Year
- 1993
- Series
- Mathematics and Its Applications Ser.
- Type
- Textbook
- Format
- Hardcover
- Language
- English
- Publication Name
- Mathematical Foundations of the State Lumping of Large Systems
- Item Length
- 9.3in
- Publisher
- Springer Netherlands
- Item Width
- 6.1in
- Item Weight
- 45.9 Oz
- Number of Pages
- X, 278 Pages
About this product
Product Information
During the investigation of large systems described by evolution equations, we encounter many problems. Of special interest is the problem of "high dimensionality" or, more precisely, the problem of the complexity of the phase space. The notion of the "comple- xity of the. phase space" includes not only the high dimensionality of, say, a system of linear equations which appear in the mathematical model of the system (in the case when the phase space of the model is finite but very large), as this is usually understood, but also the structure of the phase space itself, which can be a finite, countable, continual, or, in general, arbitrary set equipped with the structure of a measurable space. Certainly, 6 6 this does not mean that, for example, the space (R 6, ( ), where 6 is a a-algebra of Borel sets in R 6, considered as a phase space of, say, a six-dimensional Wiener process (see Gikhman and Skorokhod [1]), has a "complex structure". But this will be true if the 6 same space (R 6, ( ) is regarded as a phase space of an evolution system describing, for example, the motion of a particle with small mass in a viscous liquid (see Chandrasek- har [1]).
Product Identifiers
Publisher
Springer Netherlands
ISBN-10
0792324137
ISBN-13
9780792324133
eBay Product ID (ePID)
976804
Product Key Features
Publication Name
Mathematical Foundations of the State Lumping of Large Systems
Format
Hardcover
Language
English
Publication Year
1993
Series
Mathematics and Its Applications Ser.
Type
Textbook
Number of Pages
X, 278 Pages
Dimensions
Item Length
9.3in
Item Width
6.1in
Item Weight
45.9 Oz
Additional Product Features
Series Volume Number
264
Number of Volumes
1 Vol.
Lc Classification Number
Qa273.A1-274.9
Table of Content
1. Classes of Linear Operators.- 1.1. Basic notions.- 1.2. Closed and closable operators.- 1.3. Normally solvable operators.- 1.4. Invertibly reducible operators.- 1.5. Pseudo-resolvents.- 2. Semigroups of Operators and Markov Processes.- 2.1. Basic notions.- 2.2. Infinitesimal operators of ergodic Markov processes.- 2.3. Holomorphic semigroups with invertibly reducible infinitesimal operators.- 2.4. Semigroups of operators uniformly and strongly ergodic at the infinity.- 2.5. "Generating" operators of ergodic semi-Markov processes.- 2.6. Abstract potential operators.- 2.7. Examples of invertibly reducible operators.- 3. Perturbations of Invertibly Reducible Operators.- 3.1. Eigen-projectors and eigen-operators.- 3.2. Inversion of an invertibly reducible operator perturbed on the spectrum.- 3.3. Resolvents of singularly perturbed semigroups.- 3.4. Limit theorems and asymptotic expansions for resolvents of singularly perturbed semigroups.- 3.5. Limit theorems and asymptotic expansions for resolvents of singularly perturbed semigroups. The case of s > 2.- 4. Singular Perturbations of Holomorphic Semigroups.- 4.1. Principal problems. The method of Vishyk-Lyusternik-Vasilyeva.- 4.2. Structure of singularly perturbed semigroups.- 4.3. Regular lumped approximations to solutions of singularly perturbed equations.- 5. Asymptotic Expansions and Limit Theorems.- 5.1. Strong limits of singularly perturbed semigroups. Resolvent approach.- 5.2. Asymptotic analysis of singularly perturbed semigroups. The case of s=1.- 5.3. Asymptotic analysis of singularly perturbed semigroups.- 6. Asymptotic Phase Lumping of Markov and Semi-Markov Processes.- 6.1. Limit theorems.- 6.2. Asymptotic phase lumping. The case of s=1.- 6.3. Some examples.- 6.4. Asymptotic phase lumping. The case of s? 2.- 6.5. Classification of processes admitting asymptotic phase lumping.- 6.6. Limit theorems and asymptotic theorems for additive functionals.- 7. Applications of the Theory of Singularly Perturbed Semigroups.- 7.1. Tikhonov systems of differential equations.- 7.2. Nonrelativistic limit of the Dirac operator.- 7.3. Hydrodynamic limit for the linearized Boltzmann equation.- References.
Copyright Date
1993
Topic
Functional Analysis, Probability & Statistics / Stochastic Processes, Probability & Statistics / General, Applied
Lccn
93-014333
Dewey Decimal
515.7246
Intended Audience
Scholarly & Professional
Dewey Edition
20
Illustrated
Yes
Genre
Mathematics
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eBay item number:386711277418
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