國立虎尾科技大學 |

Transfer Operators, Endomorphisms, and Measurable Partitions

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Transfer Operators, Endomorphisms, and Measurable Partitions/ by Sergey Bezuglyi, Palle E. T. Jorgensen.
作者:	Bezuglyi, Sergey.
其他作者:	Jorgensen, Palle E. T.
面頁冊數:	X, 162 p. 7 illus.online resource. :
Contained By:	Springer Nature eBook
標題:	Measure theory. -
電子資源:	https://doi.org/10.1007/978-3-319-92417-5
ISBN:	9783319924175

Transfer Operators, Endomorphisms, and Measurable Partitions
Bezuglyi, Sergey.

Transfer Operators, Endomorphisms, and Measurable Partitions[electronic resource] /by Sergey Bezuglyi, Palle E. T. Jorgensen. - 1st ed. 2018. - X, 162 p. 7 illus.online resource. - Lecture Notes in Mathematics,22170075-8434 ;. - Lecture Notes in Mathematics,2144.

1. Introduction and Examples -- 2. Endomorphisms and Measurable Partitions -- 3. Positive, and Transfer, Operators on Measurable Spaces: general properties -- 4.Transfer Operators on Measure Spaces -- 5. Transfer operators on L1 and L2 -- 6. Actions of Transfer Operators on the set of Borel Probability Measures -- 7. Wold’s Theorem and Automorphic Factors of Endomorphisms -- 8. Operators on the Universal Hilbert Space Generated by Transfer Operators -- 9. Transfer Operators with a Riesz Property -- 10. Transfer Operators on the Space of Densities -- 11. Piecewise Monotone Maps and the Gauss Endomorphism -- 12. Iterated Function Systems and Transfer Operators -- 13. Examples.

The subject of this book stands at the crossroads of ergodic theory and measurable dynamics. With an emphasis on irreversible systems, the text presents a framework of multi-resolutions tailored for the study of endomorphisms, beginning with a systematic look at the latter. This entails a whole new set of tools, often quite different from those used for the “easier” and well-documented case of automorphisms. Among them is the construction of a family of positive operators (transfer operators), arising naturally as a dual picture to that of endomorphisms. The setting (close to one initiated by S. Karlin in the context of stochastic processes) is motivated by a number of recent applications, including wavelets, multi-resolution analyses, dissipative dynamical systems, and quantum theory. The automorphism-endomorphism relationship has parallels in operator theory, where the distinction is between unitary operators in Hilbert space and more general classes of operators such as contractions. There is also a non-commutative version: While the study of automorphisms of von Neumann algebras dates back to von Neumann, the systematic study of their endomorphisms is more recent; together with the results in the main text, the book includes a review of recent related research papers, some by the co-authors and their collaborators.

ISBN: 9783319924175

Standard No.: 10.1007/978-3-319-92417-5doiSubjects--Topical Terms:

527848
Measure theory.

LC Class. No.: QA312-312.5

Dewey Class. No.: 515.42

Transfer Operators, Endomorphisms, and Measurable Partitions
LDR:03445nam a22004095i 4500 001 995228
003 DE-He213
005 20200706015833.0
007 cr nn 008mamaa
008 201225s2018 gw | s |||| 0|eng d
020 $a 9783319924175 $9 978-3-319-92417-5
024 7 $a 10.1007/978-3-319-92417-5 $2 doi
035 $a 978-3-319-92417-5
050 4 $a QA312-312.5
072 7 $a PBKL $2 bicssc
072 7 $a MAT034000 $2 bisacsh
072 7 $a PBKL $2 thema
082 0 4 $a 515.42 $2 23
100 1 $a Bezuglyi, Sergey. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1206445
245 1 0 $a Transfer Operators, Endomorphisms, and Measurable Partitions $h [electronic resource] / $c by Sergey Bezuglyi, Palle E. T. Jorgensen.
250 $a 1st ed. 2018.
264 1 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2018.
300 $a X, 162 p. 7 illus. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
490 1 $a Lecture Notes in Mathematics, $x 0075-8434 ; $v 2217
505 0 $a 1. Introduction and Examples -- 2. Endomorphisms and Measurable Partitions -- 3. Positive, and Transfer, Operators on Measurable Spaces: general properties -- 4.Transfer Operators on Measure Spaces -- 5. Transfer operators on L1 and L2 -- 6. Actions of Transfer Operators on the set of Borel Probability Measures -- 7. Wold’s Theorem and Automorphic Factors of Endomorphisms -- 8. Operators on the Universal Hilbert Space Generated by Transfer Operators -- 9. Transfer Operators with a Riesz Property -- 10. Transfer Operators on the Space of Densities -- 11. Piecewise Monotone Maps and the Gauss Endomorphism -- 12. Iterated Function Systems and Transfer Operators -- 13. Examples.
520 $a The subject of this book stands at the crossroads of ergodic theory and measurable dynamics. With an emphasis on irreversible systems, the text presents a framework of multi-resolutions tailored for the study of endomorphisms, beginning with a systematic look at the latter. This entails a whole new set of tools, often quite different from those used for the “easier” and well-documented case of automorphisms. Among them is the construction of a family of positive operators (transfer operators), arising naturally as a dual picture to that of endomorphisms. The setting (close to one initiated by S. Karlin in the context of stochastic processes) is motivated by a number of recent applications, including wavelets, multi-resolution analyses, dissipative dynamical systems, and quantum theory. The automorphism-endomorphism relationship has parallels in operator theory, where the distinction is between unitary operators in Hilbert space and more general classes of operators such as contractions. There is also a non-commutative version: While the study of automorphisms of von Neumann algebras dates back to von Neumann, the systematic study of their endomorphisms is more recent; together with the results in the main text, the book includes a review of recent related research papers, some by the co-authors and their collaborators.
650 0 $a Measure theory. $3 527848
650 0 $a Functional analysis. $3 527706
650 0 $a Mathematical statistics. $3 527941
650 0 $a Probabilities. $3 527847
650 0 $a Thermodynamics. $3 596513
650 0 $a Operator theory. $3 527910
650 1 4 $a Measure and Integration. $3 672015
650 2 4 $a Functional Analysis. $3 672166
650 2 4 $a Probability and Statistics in Computer Science. $3 669886
650 2 4 $a Probability Theory and Stochastic Processes. $3 593945
650 2 4 $a Operator Theory. $3 672127
700 1 $a Jorgensen, Palle E. T. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 882204
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9783319924168
776 0 8 $i Printed edition: $z 9783319924182
830 0 $a Lecture Notes in Mathematics, $x 0075-8434 ; $v 2144 $3 1254300
856 4 0 $u https://doi.org/10.1007/978-3-319-92417-5
912 $a ZDB-2-SMA
912 $a ZDB-2-SXMS
912 $a ZDB-2-LNM
950 $a Mathematics and Statistics (SpringerNature-11649)
950 $a Mathematics and Statistics (R0) (SpringerNature-43713)