Author | Donoghue, William F. author |
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Title | Monotone Matrix Functions and Analytic Continuation [electronic resource] / by William F. Donoghue |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1974 |
Connect to | http://dx.doi.org/10.1007/978-3-642-65755-9 |
Descript | X, 184 p. online resource |
I. Preliminaries -- II. Pick Functions -- III. Pick Matrices and Loewner Determinants -- IV. Fatou Theorems -- V. The Spectral Theorem -- VI. One-Dimensional Perturbations -- VII. Monotone Matrix Functions -- VIII. Sufficient Conditions -- IX. Loewnerโs Theorem -- X. Reproducing Kernels -- XI. Nagy-Koranyi Proof of Loewnerโs Theorem -- XII. The Cauchy Interpolation Problem -- XIII. Interpolation by Pick Functions -- XIV. The Interpolation of Monotone Matrix Functions -- XV. Almost Positive Matrices -- XVI. The Analytic Continuation of Bergman Kernels -- XVII. The Loewner-FitzGerald Theorem -- XVIII. Loewnerโs Differential Equation -- XIX. More Analytic Continuation -- Notes and Comment