Principal currents were invented to provide a non commutative spectral theory in which there is still significant localization. These currents are often integral and are associated with a vector field and an integer-valued weight which plays the role of a multi-operator index. The study of principal currents involves scattering theory, new geometry associated with operator algebras, defect spaces associated with Wiener-Hopf and other integral operators, and the dilation theory of contraction operators. This monograph explores the metric geometry of such currents for a pair of unitary operators and certain associated contraction operators. Applications to Toeplitz, singular integral, and differential operators are included.
Reihe
Sprache
Verlagsort
Zielgruppe
Für höhere Schule und Studium
Für Beruf und Forschung
Maße
Höhe: 255 mm
Breite: 180 mm
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ISBN-13
978-0-8218-2609-6 (9780821826096)
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Schweitzer Klassifikation
Introduction The geometry associated with eigenvalues The dilation space solution of the symbol Riemann Hilbert problem The principal current for the operator-tuple $\{P_1, P_2, W_1, W_2\}$ Estimates The criterion for eigenvalues The $N(\omega)$ operator The characteristic operator function of $T_1$ Localization and the ""cut-down"" property The joint essential spectrum Singular integral representations Toeplitz operators with unimodular symbols $C_{11}$-Contraction operators with $(1,1)$ deficiency indices Appendix A Appendix B Appendix C References.
