LEADER 04293nam  22007695  450 
001 9910863117703321
005 20240619145128.0
010   $a981-15-6225-3
024 7 $a10.1007/978-981-15-6225-9
035   $a(CKB)4100000011409333
035   $a(MiAaPQ)EBC6322004
035   $a(DE-He213)978-981-15-6225-9
035   $a(PPN)269147853
035   $a(EXLCZ)994100000011409333
100   $a20200829d2020      u|         0
101 0 $aeng
135   $aurcnu||||||||
181   $ctxt$2rdacontent
182   $cc$2rdamedia
183   $acr$2rdacarrier
200 10$aSpectral Theory of Dynamical Systems $eSecond Edition /$fby Mahendra Nadkarni
205   $aSecond edition.
210   $cSpringer Singapore$d2020
210  1$aSingapore :$cSpringer Singapore :$cImprint: Springer,$d2020.
215   $a1 online resource (223 pages)
225 1 $aTexts and Readings in Mathematics,$x2366-8717 ;$v15
311   $a981-15-6224-5 
327   $aThe Hahn-Hellinger Theorem -- The Spectral Theorem for Unitary Operators -- Symmetry and Denseness of the Spectrum -- Multiplicity and Rank -- The Skew Product -- A Theorem of Helson and Parry -- Probability Measures on the Circle Group -- Baire Category Theorems of Ergodic Theory -- Translations of Measures on the Circle -- B. Host's Theorem -- L? Eigenvalues of Non-Singular Automorphisms -- Generalities on Systems of Imprimitivity -- Dual Systems of Imprimitivity -- Saturated Subgroups of the Circle Group -- Riesz Products As Spectral Measures -- Additional Topics -- Calculus of Generalized Riesz Products.
330   $aThis book discusses basic topics in the spectral theory of dynamical systems. It also includes two advanced theorems, one by H. Helson and W. Parry, and another by B. Host. Moreover, Ornstein?s family of mixing rank-one automorphisms is given with construction and proof. Systems of imprimitivity and their relevance to ergodic theory are also examined. Baire category theorems of ergodic theory, scattered in literature, are discussed in a unified way in the book. Riesz products are introduced and applied to describe the spectral types and eigenvalues of rank-one automorphisms. Lastly, the second edition includes a new chapter ?Calculus of Generalized Riesz Products?, which discusses the recent work connecting generalized Riesz products, Hardy classes, Banach's problem of simple Lebesgue spectrum in ergodic theory and flat polynomials.
410  0$aTexts and Readings in Mathematics,$x2366-8717 ;$v15
606   $aDynamics
606   $aErgodic theory
606   $aOperator theory
606   $aTopology
606   $aGroup theory
606   $aAlgebra
606   $aField theory (Physics)
606   $aStatistical physics
606   $aDynamical Systems and Ergodic Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M1204X
606   $aOperator Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M12139
606   $aTopology$3https://scigraph.springernature.com/ontologies/product-market-codes/M28000
606   $aGroup Theory and Generalizations$3https://scigraph.springernature.com/ontologies/product-market-codes/M11078
606   $aField Theory and Polynomials$3https://scigraph.springernature.com/ontologies/product-market-codes/M11051
606   $aStatistical Physics and Dynamical Systems$3https://scigraph.springernature.com/ontologies/product-market-codes/P19090
615  0$aDynamics.
615  0$aErgodic theory.
615  0$aOperator theory.
615  0$aTopology.
615  0$aGroup theory.
615  0$aAlgebra.
615  0$aField theory (Physics).
615  0$aStatistical physics.
615 14$aDynamical Systems and Ergodic Theory.
615 24$aOperator Theory.
615 24$aTopology.
615 24$aGroup Theory and Generalizations.
615 24$aField Theory and Polynomials.
615 24$aStatistical Physics and Dynamical Systems.
676   $a515.7222
700   $aNadkarni$b Mahendra$4aut$4http://id.loc.gov/vocabulary/relators/aut$0866394
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910863117703321
996   $aSpectral Theory of Dynamical Systems$91933730
997   $aUNINA