One 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 n...
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ISBN:
(数字)9783034854696
ISBN:
(纸本)9783034854719
One 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.
The first of the annual operatortheory conferences in Ti mi~oara held four years ago was a meeting of operatortheory spe cialists from the National Institute for Scientific and Techni cal Creation ...
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ISBN:
(数字)9783034854566
ISBN:
(纸本)9783764312442
The first of the annual operatortheory conferences in Ti mi~oara held four years ago was a meeting of operatortheory spe cialists from the National Institute for Scientific and Techni cal Creation in Bucharest and from the University of Timi~oara. Since then, the participation to these conferences has greatly increased, by being attended first by operator theorists from allover the country and (since 1978) by an increasing number of foreign mathematicians. Thus the 1980 Conference can be regarded as a truly international operatortheory meeting, fifteen coun tries being represented at it. These conferences are conceived as a means to promote the cooperation between specialists in all areas of operatortheory. Among the main topics in 1980 were: dilation theory, invariant subspaces, connections with the theory of cX-algebras, subnormal operators, multidimensional functional calculus etc. Though not included in this volume, we would like to mention that in 1980 some special sessions concerning other fields of Functional Ana lysis were organized at the operatortheory conference. The research contracts of the Department of Mathematics of INCREST with the National Council for Sciences and Technoloa,y of Romania provided the means for developping the research activi ty in Functional Analysis; these contracts constitute the gene rous framework for these meetings.
"Functional Analysis" is a comprehensive, 2-volume treatment of a subject lying at the core of modern analysis and mathematical physics. The first volume reviews basic concepts such as the measure, the integ...
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ISBN:
(数字)9783034891851
ISBN:
(纸本)9783764353445;9783034899390
"Functional Analysis" is a comprehensive, 2-volume treatment of a subject lying at the core of modern analysis and mathematical physics. The first volume reviews basic concepts such as the measure, the integral, Banach spaces, bounded operators and generalized functions. Volume II moves on to more advanced topics including unbounded operators, spectral decomposition, expansion in generalized eigenvectors, rigged spaces, and partial differential operators. This text provides students of mathematics and physics with a clear introduction into the above concepts, with the theory well illustrated by a wealth of examples. Researchers will appreciate it as a useful reference manual.
This volume is dedicated to Leonid Lerer on the occasion of his seventieth birthday. The main part presents recent results in Lerer’s research area of interest, which includes Toeplitz, Toeplitz plus Hankel, and Wien...
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ISBN:
(数字)9783034806398
ISBN:
(纸本)9783034806381;9783034807982
This volume is dedicated to Leonid Lerer on the occasion of his seventieth birthday. The main part presents recent results in Lerer’s research area of interest, which includes Toeplitz, Toeplitz plus Hankel, and Wiener-Hopf operators, Bezout equations, inertia type results, matrix polynomials, and related areas in operator and matrix theory. Biographical material and Lerer's list of publications complete the volume.
The contributions in this volume are dedicated to Vladimir G. Maz'ya and are par tially based on talks given at the conference "Functional Analysis, Partial Differ ential Equations, and Applicatio...
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ISBN:
(数字)9783034886758
ISBN:
(纸本)9783764362010;9783034897266
The contributions in this volume are dedicated to Vladimir G. Maz'ya and are par tially based on talks given at the conference "Functional Analysis, Partial Differ ential Equations, and applications", which took place at the University of Rostock from August 31 to September 4, 1998, to honour Prof. Maz'ya. This conference (a satellite meeting of the ICM) gave an opportunity to many friends and colleagues from all over the world to honour him. This academic community is very large. The scientific field of Prof. Maz'ya is impressively broad, which is reflected in the variety of contributions included in the volumes. Vladimir Maz'ya is the author and co-author of many publications (see the list of publications at the end of this volume), the topics of which extend from functional analysis, function theory and numerical analysis to partial differential equations and their broad applications. Vladimir G. Maz'ya provided significant contributions, among others to the the ory of Sobolev spaces, the capacity theory, boundary integral methods, qualitative and asymptotic methods of analysis of linear and nonlinear elliptic differential equations, the Cauchy problem for elliptic and hyperbolic equations, the theory of multipliers in spaces of differentiable functions, maximum principles for elliptic and parabolic systems, and boundary value problems in domains with piecewise smooth boundaries. Surveys on Maz'ya's work in different fields of mathematics and areas, where he made essential contributions, form a major part of the present first volume of The Maz'ya Anniversary Collection.
This book gives a gentle but up-to-date introduction into the theory of operator semigroups (or linear dynamical systems), which can be used with great success to describe the dynamics of complicated phenomena ar...
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ISBN:
(数字)9783319428130
ISBN:
(纸本)9783319428116;9783319826707
This book gives a gentle but up-to-date introduction into the theory of operator semigroups (or linear dynamical systems), which can be used with great success to describe the dynamics of complicated phenomena arising in many applications. Positivity is a property which naturally appears in physical, chemical, biological or economic processes. It adds a beautiful and far reaching mathematical structure to the dynamical systems and operators describing these processes.;In the first part, the finite dimensional theory in a coordinate-free way is developed, which is difficult to find in literature. This is a good opportunity to present the main ideas of the Perron-Frobenius theory in a way which can be used in the infinite dimensional situation. applications to graph matrices, age structured population models and economic models are discussed.;The infinite dimensional theory of positive operator semigroups with their spectral and asymptotic theory is developed in the second part. Recent applications illustrate the theory, like population equations, neutron transport theory, delay equations or flows in networks. Each chapter is accompanied by a large set of exercises. An up-to-date bibliography and a detailed subject index help the interested reader.;The book is intended primarily for graduate and master students. The finite dimensional part, however, can be followed by an advanced bachelor with a solid knowledge of linear algebra and calculus.
This volume contains the proceedings of the International Workshop on operatortheory and applications held at the University of Algarve in Faro, Portugal, September 12-15, in the year 2000. The main topics of the con...
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ISBN:
(数字)9783034880077
ISBN:
(纸本)9783764369477;9783034894012
This volume contains the proceedings of the International Workshop on operatortheory and applications held at the University of Algarve in Faro, Portugal, September 12-15, in the year 2000. The main topics of the conference were !> Factorization theory; !> Factorization and Integrable Systems; !> operator Theoretical Methods in Diffraction theory; !> Algebraic Techniques in operatortheory; !> applications to Mathematical Physics and Related Topics. A total of 94 colleagues from 21 countries participated in the conference. The major part of participants came from Portugal (32), Germany (17), Israel (6), Mexico (6), the Netherlands (5), USA (4) and Austria (4). The others were from Ukraine, Venezuela (3 each), Spain, Sweden (2 each), Algeria, Australia, Belorussia, France, Georgia, Italy, Japan, Kuwait, Russia and Turkey (one of each country). It was the 12th meeting in the framework of the IWOTA conferences which started in 1981 on an initiative of Professors 1. Gohberg (Tel Aviv) and J. W. Helton (San Diego). Up to now, it was the largest conference in the field of operatortheory in Portugal.
The operatortheory conferences, organized by the Department of Mathematics of INCREST and the Department of Mathematics of the University of Timi~oara, are conceived as a means to promote cooperation and exchange of ...
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ISBN:
(数字)9783034872508
ISBN:
(纸本)9783764323431;9783034872522
The operatortheory conferences, organized by the Department of Mathematics of INCREST and the Department of Mathematics of the University of Timi~oara, are conceived as a means to promote cooperation and exchange of information between specialists in all areas of operatortheory. This book comprises carefully selected papers on theory of linear operators and related fields. Original results of new research in fast developing areas are included. Several contributed papers focus on the action of linear operators in various function spaces. Recent advances in spectral theory and related topics, operators in indefinite metric spaces, dual algebras and the invariant subspace problem, operator algebras and group representations as well as applications to mathematical physics are presented. The research contacts of the Department of :viathematics of INCREST with the National Committee for Science and Technology of Romania provided means for developing the research activity in mathematics; they represent the generous framework of these meetings too. It is our pleasure to acknowledge the financial support of UNESCO which also contributed to the success of this meeting. We are indebted to Professor Israel Gohberg for including these Proceedings in the OT Series and for valuable advice in the editing process. Birkhauser Verlag was very cooperative in publishing this volume. Camelia Minculescu, Iren Nemethi and Rodica Stoenescu dealt with the difficult task of typing the whole manuscript using a Rank Xerox 860 word processor; we thank them for this exellent job.
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