Nonselfadjoint Operators and Related Topics: Workshop on Operator Theory and Its Applications, Beersheva, February 24–28, 1992
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Basel
Birkhäuser Basel
1994
|
| Schriftenreihe: | Operator Theory: Advances and Applications
73 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Our goal is to find Grabner bases for polynomials in four different sets of expressions: 1 x- , (1 - x)-1 (RESOL) X, 1 x- (1 - xy)-1 (EB) X, , y-1, (1-yx)-1 y, (1_y)-1 (1-x)-1 (preNF) (EB) plus and (1 - xy)1/2 (1 - yx )1/2 (NF) (preNF) plus and Most formulas in the theory of the Nagy-Foias operator model [NF] are polynomials in these expressions where x = T and y = T*. Complicated polynomials can often be simplified by applying "replacement rules". For example, the polynomial (1 - xy)-2 - 2xy(1-xy)-2 + xy2 (1 - xy)-2 -1 simplifies to O. This can be seen by three applications of the replacement rule (1-xy) -1 xy -t (1 - xy)-1 -1 which is true because of the definition of (1-xy)-1. A replacement rule consists of a left hand side (LHS) and a right hand side (RHS). The LHS will always be a monomial. The RHS will be a polynomial whose terms are "simpler" (in a sense to be made precise) than the LHS. An expression is reduced by repeatedly replacing any occurrence of a LHS by the corresponding RHS. The monomials will be well-ordered, so the reduction procedure will terminate after finitely many steps. Our aim is to provide a list of substitution rules for the classes of expressions above. These rules, when implemented on a computer, provide an efficient automatic simplification process. We discuss and define the ordering on monomials later |
| Beschreibung: | 1 Online-Ressource (X, 422 p) |
| ISBN: | 9783034885225 9783034896634 |
| DOI: | 10.1007/978-3-0348-8522-5 |
Internformat
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| 245 | 1 | 0 | |a Nonselfadjoint Operators and Related Topics |b Workshop on Operator Theory and Its Applications, Beersheva, February 24–28, 1992 |c edited by A. Feintuch, I. Gohberg |
| 264 | 1 | |a Basel |b Birkhäuser Basel |c 1994 | |
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| 490 | 0 | |a Operator Theory: Advances and Applications |v 73 | |
| 500 | |a Our goal is to find Grabner bases for polynomials in four different sets of expressions: 1 x- , (1 - x)-1 (RESOL) X, 1 x- (1 - xy)-1 (EB) X, , y-1, (1-yx)-1 y, (1_y)-1 (1-x)-1 (preNF) (EB) plus and (1 - xy)1/2 (1 - yx )1/2 (NF) (preNF) plus and Most formulas in the theory of the Nagy-Foias operator model [NF] are polynomials in these expressions where x = T and y = T*. Complicated polynomials can often be simplified by applying "replacement rules". For example, the polynomial (1 - xy)-2 - 2xy(1-xy)-2 + xy2 (1 - xy)-2 -1 simplifies to O. This can be seen by three applications of the replacement rule (1-xy) -1 xy -t (1 - xy)-1 -1 which is true because of the definition of (1-xy)-1. A replacement rule consists of a left hand side (LHS) and a right hand side (RHS). The LHS will always be a monomial. The RHS will be a polynomial whose terms are "simpler" (in a sense to be made precise) than the LHS. An expression is reduced by repeatedly replacing any occurrence of a LHS by the corresponding RHS. The monomials will be well-ordered, so the reduction procedure will terminate after finitely many steps. Our aim is to provide a list of substitution rules for the classes of expressions above. These rules, when implemented on a computer, provide an efficient automatic simplification process. We discuss and define the ordering on monomials later | ||
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Datensatz im Suchindex
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-0348-8522-5 |
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| spelling | Feintuch, Avraham Verfasser (DE-588)1158228341 aut Nonselfadjoint Operators and Related Topics Workshop on Operator Theory and Its Applications, Beersheva, February 24–28, 1992 edited by A. Feintuch, I. Gohberg Basel Birkhäuser Basel 1994 1 Online-Ressource (X, 422 p) txt rdacontent c rdamedia cr rdacarrier Operator Theory: Advances and Applications 73 Our goal is to find Grabner bases for polynomials in four different sets of expressions: 1 x- , (1 - x)-1 (RESOL) X, 1 x- (1 - xy)-1 (EB) X, , y-1, (1-yx)-1 y, (1_y)-1 (1-x)-1 (preNF) (EB) plus and (1 - xy)1/2 (1 - yx )1/2 (NF) (preNF) plus and Most formulas in the theory of the Nagy-Foias operator model [NF] are polynomials in these expressions where x = T and y = T*. Complicated polynomials can often be simplified by applying "replacement rules". For example, the polynomial (1 - xy)-2 - 2xy(1-xy)-2 + xy2 (1 - xy)-2 -1 simplifies to O. This can be seen by three applications of the replacement rule (1-xy) -1 xy -t (1 - xy)-1 -1 which is true because of the definition of (1-xy)-1. A replacement rule consists of a left hand side (LHS) and a right hand side (RHS). The LHS will always be a monomial. The RHS will be a polynomial whose terms are "simpler" (in a sense to be made precise) than the LHS. An expression is reduced by repeatedly replacing any occurrence of a LHS by the corresponding RHS. The monomials will be well-ordered, so the reduction procedure will terminate after finitely many steps. Our aim is to provide a list of substitution rules for the classes of expressions above. These rules, when implemented on a computer, provide an efficient automatic simplification process. We discuss and define the ordering on monomials later Mathematics Global analysis (Mathematics) Analysis Mathematik Operatortheorie (DE-588)4075665-8 gnd rswk-swf 1\p (DE-588)1071861417 Konferenzschrift 1992 Beer Sheva gnd-content Operatortheorie (DE-588)4075665-8 s 2\p DE-604 Gohberg, Yiśrāʿēl Z. 1928-2009 Sonstige (DE-588)118915878 oth https://doi.org/10.1007/978-3-0348-8522-5 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Feintuch, Avraham Nonselfadjoint Operators and Related Topics Workshop on Operator Theory and Its Applications, Beersheva, February 24–28, 1992 Mathematics Global analysis (Mathematics) Analysis Mathematik Operatortheorie (DE-588)4075665-8 gnd |
| subject_GND | (DE-588)4075665-8 (DE-588)1071861417 |
| title | Nonselfadjoint Operators and Related Topics Workshop on Operator Theory and Its Applications, Beersheva, February 24–28, 1992 |
| title_auth | Nonselfadjoint Operators and Related Topics Workshop on Operator Theory and Its Applications, Beersheva, February 24–28, 1992 |
| title_exact_search | Nonselfadjoint Operators and Related Topics Workshop on Operator Theory and Its Applications, Beersheva, February 24–28, 1992 |
| title_full | Nonselfadjoint Operators and Related Topics Workshop on Operator Theory and Its Applications, Beersheva, February 24–28, 1992 edited by A. Feintuch, I. Gohberg |
| title_fullStr | Nonselfadjoint Operators and Related Topics Workshop on Operator Theory and Its Applications, Beersheva, February 24–28, 1992 edited by A. Feintuch, I. Gohberg |
| title_full_unstemmed | Nonselfadjoint Operators and Related Topics Workshop on Operator Theory and Its Applications, Beersheva, February 24–28, 1992 edited by A. Feintuch, I. Gohberg |
| title_short | Nonselfadjoint Operators and Related Topics |
| title_sort | nonselfadjoint operators and related topics workshop on operator theory and its applications beersheva february 24 28 1992 |
| title_sub | Workshop on Operator Theory and Its Applications, Beersheva, February 24–28, 1992 |
| topic | Mathematics Global analysis (Mathematics) Analysis Mathematik Operatortheorie (DE-588)4075665-8 gnd |
| topic_facet | Mathematics Global analysis (Mathematics) Analysis Mathematik Operatortheorie Konferenzschrift 1992 Beer Sheva |
| url | https://doi.org/10.1007/978-3-0348-8522-5 |
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