{"product_id":"9783034854719","title":"Operator Theory: Advances and Applications","description":"\u003ch1\u003eOperator Theory: Advances and Applications\u003c\/h1\u003e \u003ch2\u003eGohberg, I.\u003c\/h2\u003e \u003cp\u003eOne of the basic interpolation problems from our point of view is the problem of building a scalar rational function if its poles and zeros with their multiplicities are given. If one assurnes that the function does not have a pole or a zero at infinity, the formula which solves this problem is (1) where Zl , \" \" Z\/ are the given zeros with given multiplicates nl, \" \" n \/ and Wb\" \" W are the given p poles with given multiplicities ml, . . . ,m , and a is an arbitrary nonzero number. p An obvious necessary and sufficient condition for solvability of this simplest Interpolation pr- lern is that Zj :f: wk(1~ j ~ 1, 1~ k~ p) and nl +. . . +n\/ = ml +. . . +m ' p The second problem of interpolation in which we are interested is to build a rational matrix function via its zeros which on the imaginary line has modulus 1. In the case the function is scalar, the formula which solves this problem is a Blaschke product, namely z z. )mi n u(z) = all = l~ (2) J ( Z+ Zj where [o] = 1, and the zj's are the given zeros with given multiplicities mj. Here the necessary and sufficient condition for existence of such u(z) is that zp :f: - Zq for 1~ ]1, q~ n.\u003c\/p\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Birkhäuser\u003c\/p\u003e \u003cp\u003ePublication Date: 2014-08-23\u003c\/p\u003e \u003cp\u003eFormat: Paperback\u003c\/p\u003e \u003cp\u003eISBN-13: 9783034854719\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-3-0348-5469-6\u003c\/p\u003e \u003cp\u003eDimensions: 244cm x170cm\u003c\/p\u003e \u003cp\u003ePages: 247\u003c\/p\u003e ","brand":"Birkhäuser Basel","offers":[{"title":"Default Title","offer_id":44422187450508,"sku":"9783034854719","price":49.49,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9783034854719.jpg?v=1775680793","url":"https:\/\/fh90cf-fv.myshopify.com\/products\/9783034854719","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}