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Solution of the Truncated Complex Moment Problem for Flat Data

Raúl E. Curto University of Iowa, Iowa City, IA
Lawrence A. Fialkow State University of New York
Available Formats:
Electronic ISBN: 978-1-4704-0147-4
Product Code: MEMO/119/568.E
52 pp
List Price: $40.00 MAA Member Price:$36.00
AMS Member Price: $24.00 Click above image for expanded view Solution of the Truncated Complex Moment Problem for Flat Data Raúl E. Curto University of Iowa, Iowa City, IA Lawrence A. Fialkow State University of New York Available Formats:  Electronic ISBN: 978-1-4704-0147-4 Product Code: MEMO/119/568.E 52 pp  List Price:$40.00 MAA Member Price: $36.00 AMS Member Price:$24.00
• Book Details

Memoirs of the American Mathematical Society
Volume: 1191996
MSC: Primary 44; 47; Secondary 15;

In this book, the authors introduce a matricial approach to the truncated complex moment problem and apply it to the case of moment matrices of flat data type, for which the columns corresponding to the homogeneous monomials in $z$ and $\bar z$ of highest degree can be written in terms of monomials of lower degree. Necessary and sufficient conditions for the existence and uniqueness of representing measures are obtained in terms of positivity and extension criteria for moment matrices.

• Chapters
• 1. Introduction
• 2. Moment matrices
• 3. Positive moment matrices and representing measures
• 4. Existence of representing measures
• 5. Extension of flat positive moment matrices
• 6. Applications
• 7. Generalizations to several variables
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Volume: 1191996
MSC: Primary 44; 47; Secondary 15;

In this book, the authors introduce a matricial approach to the truncated complex moment problem and apply it to the case of moment matrices of flat data type, for which the columns corresponding to the homogeneous monomials in $z$ and $\bar z$ of highest degree can be written in terms of monomials of lower degree. Necessary and sufficient conditions for the existence and uniqueness of representing measures are obtained in terms of positivity and extension criteria for moment matrices.