{"product_id":"9783034896634","title":"Operator Theory: Advances and Applications: Workshop on Operator Theory and Its Applications, Beersheva, February 24–28, 1992","description":"\u003ch1\u003eOperator Theory: Advances and Applications: Workshop on Operator Theory and Its Applications, Beersheva, February 24–28, 1992\u003c\/h1\u003e \u003ch2\u003eFeintuch, A.; Gohberg, I.\u003c\/h2\u003e \u003cp\u003eOur 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.\u003c\/p\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Birkhäuser\u003c\/p\u003e \u003cp\u003ePublication Date: 2012-11-01\u003c\/p\u003e \u003cp\u003eFormat: Paperback\u003c\/p\u003e \u003cp\u003eISBN-13: 9783034896634\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-3-0348-8522-5\u003c\/p\u003e \u003cp\u003eDimensions: 244cm x170cm\u003c\/p\u003e \u003cp\u003ePages: 422\u003c\/p\u003e ","brand":"Birkhäuser Basel","offers":[{"title":"Default Title","offer_id":44398490255500,"sku":"9783034896634","price":49.49,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9783034896634.jpg?v=1775680652","url":"https:\/\/fh90cf-fv.myshopify.com\/products\/9783034896634","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}