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[null,"1.","Record Nr.",null,"UNINA9910818014003321"]
[null,null,"Autore",null,"Rodman L."]
[null,null,"Titolo",null,"Abstract band method via factorization, positive and band extensions of multivariable almost periodic matrix functions, and spectral estimation / / Leiba Rodman, Ilya M. Spitkovsky, Hugo J. Woerdeman"]
[null,null,"Pubbl/distr/stampa",null,"Providence, Rhode Island : , : American Mathematical Society, , [2002]"]
[{"$nulls":4},"©2002"]
[null,null,"ISBN",null,"1-4704-0360-9"]
[null,null,"Descrizione fisica",null,"1 online resource (87 p.)"]
[null,null,"Collana",null,"Memoirs of the American Mathematical Society, , 0065-9266 ; ; number 762"]
[null,null,"Disciplina",null,"510 s"]
[{"$nulls":4},"515/.724"]
[null,null,"Soggetti",null,"Lifting theory"]
[{"$nulls":4},"Factorization (Mathematics)"]
[{"$nulls":4},"Toeplitz operators"]
[null,null,"Lingua di pubblicazione",null,"Inglese"]
[null,null,"Formato",null,"Materiale a stampa"]
[null,null,null,"Livello bibliografico","Monografia"]
[null,null,null,"Note generali","Description based upon print version of record."]
[null,null,null,"Nota di bibliografia","Includes bibliographical references (pages 67-70) and index."]
[null,null,"Nota di contenuto",null,"\"\"Contents\"\"; \"\"Chapter 1. Introduction\"\"; \"\"1.1. Abstract Band Method\"\"; \"\"1.2. Factorization\"\"; \"\"1.3. Conventions and Notation\"\"; \"\"Chapter 2. Abstract Band Method: New Variations\"\"; \"\"2.1. Nonsymmetric Band Method\"\"; \"\"2.2. Shiftable Band Structure\"\"; \"\"2.3. Stability of Band Extensions\"\"; \"\"2.4. Band Extensions: The Symmetric Case\"\"; \"\"2.5. Positive Band Extensions: Existence\"\"; \"\"2.6. Description of Positive Extensions\"\"; \"\"Chapter 3. Toeplitz and Wiener Algebras of Operator Matrices\"\"; \"\"3.1. Band Extensions for Wiener Class of Operator Valued Functions on the Unit Circle\"\""]
[{"$nulls":4},"\"\"3.2. Positive Extensions for Wiener Class of Doubly Infinite Operator Matrices\"\"\"\"3.3. Application to Cyclostationary Processes\"\"; \"\"Chapter 4. Positive Extensions in Wiener Classes of Almost Periodic Matrix Functions\"\"; \"\"4.1. Almost Periodic Functions and Statement of the Problem\"\"; \"\"4.2. Preliminaries on Almost Periodic Functions and Toeplitz Operators\"\"; \"\"4.3. Toeplitz Operators Associated with Band\"\"; \"\"4.4. Positive Extension Problem: Main Results\"\"; \"\"4.5. Point Excluding Variations\"\"; \"\"4.6. Stability of Band Extensions\"\"; \"\"4.7. Positive Measure Extension Problem\"\""]
[{"$nulls":4},"\"\"4.8. Application to Spectral Estimation for ARMA Processes\"\"\"\"Chapter 5. Appendix\"\"; \"\"5.1. Bochner-Phillips Theorem\"\"; \"\"5.2. Abstract "]
[{"$nulls":4},"Factorization\"\"; \"\"5.3. Krein's Theorem on Extension of Positive Functionals\"\"; \"\"5.4. Invertibility in Banach Algebras\"\"; \"\"Bibliography\"\"; \"\"Index\"\""]
[null,"2.","Record Nr.",null,"UNINA9910300150203321"]
[null,null,"Autore",null,"Monk J. Donald"]
[null,null,"Titolo",null,"Cardinal Invariants on Boolean Algebras : Second Revised Edition / / by J. Donald Monk"]
[null,null,"Pubbl/distr/stampa",null,"Basel : , : Springer Basel : , : Imprint : Birkhäuser, , 2014"]
[null,null,"ISBN",null,"3-0348-0730-9"]
[null,null,"Edizione",null,"[2nd ed. 2014.]"]
[null,null,"Descrizione fisica",null,"1 online resource (569 pages) : illustrations"]
[null,null,"Collana",null,"Progress in Mathematics, , 0743-1643 ; ; 142"]
[null,null,"Disciplina",null,"511.3"]
[{"$nulls":4},"511.324"]
[null,null,"Soggetti",null,"Logic, Symbolic and mathematical"]
[{"$nulls":4},"Algebra"]
[{"$nulls":4},"Ordered algebraic structures"]
[{"$nulls":4},"Mathematical Logic and Foundations"]
[{"$nulls":4},"Order, Lattices, Ordered Algebraic Structures"]
[null,null,"Lingua di pubblicazione",null,"Inglese"]
[null,null,"Formato",null,"Materiale a stampa"]
[null,null,null,"Livello bibliografico","Monografia"]
[null,null,null,"Note generali","Bibliographic Level Mode of Issuance: Monograph"]
[null,null,null,"Nota di bibliografia","Includes bibliographical references and indexes."]
[null,null,"Nota di contenuto",null,"Introduction -- 1. Special Operations on Boolean Algebras -- 2. Special Classes of Boolean Algebras -- 3. Cellularity -- 4. Depth -- 5. Topological Density -- 6. Pi-Weight -- 7. Length -- 8. Irredundance -- 9. Cardinality -- 10. Independence -- 11. Pi-Character -- 12. Tightness -- 13. Spread -- 14. Character -- 15. Hereditary Lindelöf Degree -- 16. Hereditary Density -- 17. Incomparability -- 18. Hereditary Cofinality -- 19. Number of Ultrafilters -- 20. Number of Automorphisms -- 21. Number of Endomorphisms -- 22. Number of Ideals -- 23. Number of Subalgebras -- 24. Other Cardinal Functions -- 25. Diagrams -- 26. Examples -- 27. Problems -- References -- Symbol Index -- Subject Index -- Name Index."]
[null,null,null,"Sommario/riassunto","This book is concerned with cardinal number valued functions defined for any Boolean algebra. Examples of such functions are independence, which assigns to each Boolean algebra the supremum of the cardinalities of its free subalgebras, and cellularity, which gives the supremum of cardinalities of sets of pairwise disjoint elements. Twenty-one such functions are studied in detail, and many more in passing. The questions considered are the behaviour of these functions under algebraic operations such as products, free products, ultraproducts, and their relationships to one another. Assuming familiarity with only the basics of Boolean algebras and set theory, "]
[{"$nulls":4},"through simple infinite combinatorics and forcing, the book reviews current knowledge about these functions, giving complete proofs for most facts. A special feature of the book is the attention given to open problems, of which 185 are formulated. Based on Cardinal Functions on Boolean Algebras (1990) and Cardinal Invariants on Boolean Algebras (1996) by the same author, the present work is much larger than either of these. It contains solutions to many of the open problems of the earlier volumes. Among the new topics are continuum cardinals on Boolean algebras, with a lengthy treatment of the reaping number. Diagrams at the end of the book summarize the relationships between the functions for many important classes of Boolean algebras, including interval algebras, tree algebras and superatomic algebras."]