The Moment Problem
Springer International Publishing (Verlag)
978-3-319-87817-1 (ISBN)
The Moment Problem will be particularly useful to graduate students and researchers working on moment problems, functional analysis, complex analysis, harmonic analysis, real algebraic geometry, polynomial optimization, or systems theory. With notes providing useful background information and exercises of varying difficulty illustrating the theory, this book will also serve as a reference on the subject and can be used for self-study.
Konrad Schmudgen is professor at the University of Leipzig, Germany. He discovered the strict Positivstellensatz and developed in this manner the interplay between real algebraic geometry and moment problems. He obtained a number of fundamental results on full and truncated multidimensional moment problems.
Preface and Overview.- 1 Integral representations of linear functionals.- 2 Moment problems on abelian *-semigroups.- Part I The one dimensional moment problem.- 3 One dimensional moment problems on intervals: existence.- 4 One dimensional moment problems: determinacy.- 5 Orthogonal polynomials and Jacobi operators.- 6 The operator-theoretic approach to the Hamburger moment problem.- 7 The indeterminate Hamburger moment problem.- 8 The operator-theoretic approach to the Stieltjes moment problem.- Part II The one dimensional truncated moment problem.- 9 The one-dimensional truncated Hamburger and Stieltjes moment problems.- 10 The one-dimensional truncated moment problem on a bounded interval.- 11 The moment problem on the unit circle.- Part III The multidimensional moment problem.- 12 The moment problem on compact semi-algebraic sets.- 13 The moment problem on closed semi-algebraic sets: existence.- 14 The multidimensional moment problem: determinacy.- 15 The complex moment problem.- 16 Semidefinite programming and polynomial optimization.- Part IV The multidimensional truncated moment problem.- 17 Multidimensional truncated moment problems: existence criteria.- 18 Multidimensional truncated moment problems: basic concepts and special topics.- 19 The truncated moment problem for homogeneous polynomials.
"The virtue of Schmüdgen's graduate textbook is that it lays solid foundations for any further explorations, theoretical or applied, in the complex and dynamical realm of moment problems. ... This volume will definitely be the reference to moment problems for several future generations." (Mihai Putinar,Mathematical Reviews, 2018)
"The bibliography includes many older and newer titles, the author being one of the main contributors in the last forty years. The book is well-written and it can be considered as an up-to day reference book for the use of both beginners and confirmed researchers, oriented not only to the domain of moment problems but also to other branches of analysis, or of mathematics, in general." (Florian-Horia Vasilescu, zbMATH, 2018)
Erscheinungsdatum | 08.02.2019 |
---|---|
Reihe/Serie | Graduate Texts in Mathematics |
Zusatzinfo | XXIII, 512 p. 6 illus. |
Verlagsort | Cham |
Sprache | englisch |
Maße | 155 x 235 mm |
Gewicht | 831 g |
Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
Mathematik / Informatik ► Mathematik ► Analysis | |
Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
Schlagworte | canonical solutions • Carleman condition • Hamburger moment problem • Hankel matrix • Hausdorff moment problem • Jacobi operators • moment problem on semi-algebraic sets • MSC (2010): 44A60, 14P10, 47A57 • Nevanlinna parametrization • orthogonal polynomials • polynomial optimization • Positive polynomials • Positivstellensätze • Positivstellensätze • Principal solutions • Stieltjes moment problem • Weyl circle |
ISBN-10 | 3-319-87817-4 / 3319878174 |
ISBN-13 | 978-3-319-87817-1 / 9783319878171 |
Zustand | Neuware |
Haben Sie eine Frage zum Produkt? |
aus dem Bereich