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Nagel R., Derdinger R., Günther P. — Ergodic theory in the perspective of functional analysis
Nagel R., Derdinger R., Günther P. — Ergodic theory in the perspective of functional analysis

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Название: Ergodic theory in the perspective of functional analysis

Авторы: Nagel R., Derdinger R., Günther P.


In the present book we develop the most important and basic results of modern ergodic theory thin the more comprehensive framework of functional analysis. Methods of functional analysis often make it possible to formulate more general results, which elucidate structural similarities of problems arising in different branches of ergodic theory. The 13 Lectures together with the Dicossions (and the Introductory Appendices if necessary) should provide a compact introduction into modern ergodic theory for the newcomer. rhe book will be, however, much easier to comprehend for students with a solid background in functional analysis.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1987

Количество страниц: 354

Добавлена в каталог: 08.12.2005

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Предметный указатель
$(n,\varepsilon)$-net      XIII/1
$F_{\sigma}$-set      W/14
$G_{\delta}$-set      X/15
$\lambda$-distinguishable      Z/19
$\mu$-entropy      XII/2
$\mu$-information      XI/3
a-adic solenoid      VII/13
Abel averages      W/2
Absolute value (of a function)      C/1
Absolute value (of an operator)      X/6
Absolutely continuous measure      A/3
Adid (= asymptotically decressingn input dependence)      Z/16
Affine transformation      XIII/11
Almost all      A/2
Almost everywhere (= $\mu$-almost everywhere = $\mu$-a.e.)      A/2
Alphabet (of a source)      Z/7
Amenable      Y/3
Antiperiodic      X/1
Approximate point spectrum      B/6
Arithmetic progression      III/14
Baker's transformation      II/2 VI/7
Banach algebra      II/8
Banach lattice      C/2
Banach space      B/1
Banach's principle      V/5
Band      IV/22
Band component      IV/22
Bernoulli shift      II/3
bi-Markov operator      II/13
bi-measure-preserving      II/1a
bi-stochastic      IX/9
Binary symmetric channel      Z/13
Bit      Z/5
Block      Z/7
Block coding      Z/18
Borel algebra      A/4
Borel measure      A/4
Borel set      A/4
Bounded (linear) operator      B/2
Bounded sets of operators      B/3
C*-algebra      C/3
Capacity      Z/11
Category      A/2
Cesaro means      IV/1 IV/1a
Cesaro summable      E/1
Channel      Z/7
Channel, space      Z/8
Character group      D/1
Characteristic function      A/5
Common refinement      XI/1
Compact      A/1
Compact group      D/1
Compact operator      VI/4
Compact right topological semigroup      VII/15
Compact semigroup      VII/1
Complete system of isomorphism invariants      VI/6
Compound channel      Z/9
Conditional $\mu$-information      XI/8
Conditional expectation operator      B/8 IV/4
Conditional information      Z/6
Conditional probability      XI/7 Z/5
Conservative      V/11
Contraction      B/2
Convergence in p-norm      A/6
Convergence in p-norm, $\mu$ almost everywhere      A/6
Convergence in p-norm, $\mu$ stochastically (= in measure)      A/6
Countable Lebesgue spectrum      VI/12
Countably generated      A/4
Cover (= finite cover)      XI/1 XI/13
Covering lemma of Lebesgue      A/1
Cyclic (spectrum)      VI/9
Dedekind completion      IX/16
Density (of a sequence)      E/1 IX/4
Dependence (of covers)      XII/14
Deterministic channel      Z/9
Differentiable dynamical system (DDS)      II/1
Differential equation      II/16
Diffuse measure      X/19
Dirac measure      B/6
Direct sum (of Banach spaces)      B/9
Discrete spectrum      VII/6 VIII/1
Disjoint cover (= finite partition)      XI/3
Disjointification      XI/5 XI/7
Dissipative      V/11
Distance (of covers)      XI/9
Distribution (of a Bernoulli shift)      II/3
Distribution (of a Markov shift)      II/7 II/14
Distributive lattice      XI/13
Doeblin condition      W/10
Dominated estimate      V/2
Doubly stochastic operator      II/13
Dual Banach space      B/1
Dual group      D/1
Dual norm      B/1
Dual unit ball      B/2
Dyadic interval      A/4
Eigenfunction      VI/9
Eigenspace      B/6
Eigenvalue      B/6
entropy      III/6a XII/2
Enveloping semigroup      VII/14 VII/16
Equidietribution      IV/13
Equivalence class (of measurable functions)      B/7
Equivalent measure      A/3
Ergodic      III/2
Ergodic channel      Z/11
Ergodic component      III/9
Ergodic hypothesis      I/3 III/8b III/18 V/4
Ergodic measure      IV/20
Expected value      V/18
Extension theorem (for set functions)      A/7
Extremally disconnected      VI/14
Extreme point      B/2
Faithful (= strictly positive)      Y/7
Finer (= comparison of covers)      XI/1
Finer... up to $\varepsilon$ (= comparison of covers)      XII/5
Finite ($\sigma$-finite) measure space      A/2
Finite intersection property      A/1
First category      A/2
Fixed space      III/2a
Flow      II/16
Functional-analytic dynamical system (= FDS)      II/1a
General shift      XII/11
Generated Boolean ($\sigma$-)algebra      A/4
Generating element      VII/8
Generating set of covers      XII/5
Generator (= generating cover)      XII/5
Generator (of a semigroup)      IV/34
Geometry      B/2
GNS-Hilbert space      Y/7
Grothendieck space      W/14
Haar measure      D/1
Hamiltonian flow      II/17
Hilbert space isomorphism (= spectral isomorphism)      VI/3a
Ideal (of a semigroup)      VII/2
Identically distributed      V/18
Independent      V/18
Individually ergodic      V/1
Induced operator      II/4
Infinum      C/1
information      Z/2
Information rate      Z/7
Input alphabet      Z/7
Input alphabet probability      Z/8
Input alphabet space      Z/7
Intrinsically ergodic      XIII/9
Invariant measure      II/1a IV/20
Invariant set      III/8
Involution      C/3
Irreducible (= indecomposable) matrix      III/15 IV/13a
Irreducible (= indecomposable) operator      III/15 IV/13a
Isomorphism invariant      VI/5 VI/7
Isomorphism of MDS's (= algebra isomorphism)      VI/1
Isomorphism of TDS's      VI/3a
Isomorphism problem      VI/5
Jointly continuous (multiplication)      VII/7
K-partition      XII/14
K-system      XII/16
Kakutani decomposition      V/17
Kernel operator      IV/5a X/2
Kolmogorov's 0-1-law      XII/15
Lattice dilation      II/15 U/1
Lattice homomorphism      C/2
Lattice ideal      III/15
Lebesgue space      X/19
Left amenable      Y/3
letter      Z/7
Lifting      VI/6a
m-informstion      XI/13
Markov operator      II/13
Markov process      X/1
Markov shift      II/7 II/14
Martingale convergence theorem      Y/10
Maximal ergodijc inequality      V/2
Maximal ergodijc lemma      V/2
Mean ergodic operator      IV/1a
Mean ergodic semigroup      IV/10 IV/34 Y/1
Measurable mapping      A/4
Measurable rectangle      A/6
Measure      A/2
Measure, algebra      A/3 VI/1
Measure, preserving      A/4
Measure, space      A/2
Measure, theoretical dynamical system (= FiDS)      II/1a
Memoryless      Z/12
Minimal      III4
Mixing cover      XII/14
Modular operator      V/7
Monothetic      VII/8
Multiplication of operators      B/5
Multiplication operator      C/3
Multiplicative operator      C/4
Neumann's series      B/6
Non-singular      IV/21
Normal number      V/B
Normal state (= order continuous state)      Y/9
Normalized Haar_measure      D/1
Nowhere dense (= rare)      A/2
Null set (= $\mu$-null set)      A/2
Observable      I/3
One-dimensional operator $f \bigotimes f'$      B/2
Open rectangle      A/1
Operator norm      B/2
Orbit      III/4 III/B
Order bounded      C/2
Order complete      C/2
Order continuous      C/2
Order convergent      V/9
Order interval      C/2
Ordered cover      XI/6
Ordering      XI/6
Orthogonal band      IV/22
Orthogonal band operators      X/6
Output alphabet      Z/7
Output probability      Z/8
Output space      Z/8
p-adic integers      VIII/9
p-integrable function      A/6
p-Prufer group      VIII/11
Partially periodic      X/3
Periodic point      X/1
Periodic transformation      X/1
Piecewise $C^2$-function      IV/23
Point isomorphism      VI/4
Point spectrum      B/5
Pole (of the resolvent)      W/2
Positive cone      C/1
Positive dilation      U/1
Positive function      C/1
Positive operator      C/2
Principle of uniform boundedness      B/3
Probability measure      A/2
Probability of error      Z/18
Probability space      A/2
Product (measure) space      A/7
Product (of functions)      C/3
Product space (topological)      A/1
Projection      B/2
Quasi-compact operator      W/5
Radon measure      B/6
Random variable      V/18
Recurrent      III/1 III/12
Reducible      IV/13a
Reflexive      B/2
Regular Borel measure      A/4
Regular norm      V/20
Regular operator      V/20
Resolvent      B/5
Resolvent set      B/5
Right amenable      Y/3
Rohlin's lemma      X/2
Rohlin-distance      XI/9
Rotation      II/2
Rotation operator      IV/7
Second category      A/2
Second law of thermodynamics      III/6a III/16
Semigroup      VII/1
Semitopological semigroup      VII/1
Separable      B/5
Separately continuous (multiplication)      VII/1 VII/7
Separating base      A/4 X/11
Shannon's information      Z/2
Shift      II/2 II/3
Simple eigenvalue      B/6
Source (= information source)      Z/7
Spectral isomorphism      VI/3a
Spectral radius      B/6
Spectral theorem      VI/10
Spectral theory      B/5
Spectrum      B/5
Speed of convergeince      IV/18
Stacking method      X/7
State      I/3 II/1
State space      I/3 II/5 II/19
Stationary channel      Z/11
Stationary source      Z/11
Stochastic matrix      II/5
Stochastic operator      II/12
Stone — Cech compactification      C/4
Stone — Cech representation space      C/4 VI/14
Strong Law of Large Numbers      V/7 V/18
Strong metric      X/14
Strong operator topology      B/2
Strongly continuous semigroup      IV/34
Strongly ergodic      IX/9
Strongly mixing      IX/2
Subshift of finite type      XIII/B
Supremum      C/1
Symbol      Z/7
Symmetric difference      A/3
t-information      XI/2
T-invariant set      IV/13a
Theorem of Akcoglu      V/6
Theorem of Akcoglu — Sucheston      IX/11
Theorem of Alaoglu — Bourbaki      B/2
Theorem of Baire      A/2
Theorem of Birkhoff      V/1
Theorem of Blum — Hanson      IX/11
Theorem of Borel      V/8
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