02821nam a22003378i 4500001001600000003000700016008004100023020001800064020001800082035002000100041000800120082001600128100002800144245013500172264007100307300003900378336002600417337002600443338003600469490006700505500001300572505060600585520100001191650004602191650002402237700002402261856005502285932003202340596000602372949010502378CR9781139093514UkCbUP110523s2012||||enk o ||1 0|eng|d a9781139093514 a9781107018877 a(Sirsi) a794782 aeng00a515/.452231 aArov, Damir Z.,eauthor10aBitangential direct and inverse problems for systems of integral and differential equationsh[E-Book] /cDamir Z. Arov, Harry Dym. 1aCambridge :bCambridge University Press,c2012e(CUP)fCUP20200108 a1 online resource (xiv, 472 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier aEncyclopedia of mathematics and its applications ;vvolume 145 aenglisch0 aIntroduction -- Canonical systems and related differential equations -- Matrix-valued functions in the Nevanlinna class -- Interpolation problems, resolvent matrices and de Branges spaces -- Chains that are matrizants and chains of associated pairs -- The bitangential direct input scattering problems -- Bitangential direct input impedance and spectral problems -- Inverse monodromy problems -- Bitangential Krein extension problems -- Bitangential inverse input scattering problems -- Bitangential inverse input impedance and spectral problems -- Direct and inverse problems for Dirac-Krein systems. aThis largely self-contained treatment surveys, unites and extends some 20 years of research on direct and inverse problems for canonical systems of integral and differential equations and related systems. Five basic inverse problems are studied in which the main part of the given data is either a monodromy matrix; an input scattering matrix; an input impedance matrix; a matrix valued spectral function; or an asymptotic scattering matrix. The corresponding direct problems are also treated. The book incorporates introductions to the theory of matrix valued entire functions, reproducing kernel Hilbert spaces of vector valued entire functions (with special attention to two important spaces introduced by L. de Branges), the theory of J-inner matrix valued functions and their application to bitangential interpolation and extension problems, which can be used independently for courses and seminars in analysis or for self-study. A number of examples are presented to illustrate the theory. 0aInverse problems (Differential equations) 0aIntegral equations.1 aDym, Harry,eauthor40uhttps://doi.org/10.1017/CBO9781139093514zVolltext aCambridgeCore (Order 30059) a1 aXX(794782.1)wAUTOc1i794782-1001lELECTRONICmZBrNsYtE-BOOKu8/1/2020xUNKNOWNzUNKNOWN1ONLINE