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Books > Science & Mathematics > Physics > Quantum physics (quantum mechanics)
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Characteristic Functions and Models of Nonself-Adjoint Operators (Paperback, Softcover reprint of the original 1st ed. 1996)
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Characteristic Functions and Models of Nonself-Adjoint Operators (Paperback, Softcover reprint of the original 1st ed. 1996)
Series: Mathematics and Its Applications, 349
Expected to ship within 18 - 22 working days
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Over the last decades, the study of nonself-adjoint or nonunitary
operators has been mainly based on the method of characteristic
functions and on methods of model construction or dilatation for
corresponding operator classes. The characteristic function is a
mathematical object (a matrix or an operator) associated with a
class of nonself-adjoint (or nonunitary) operators that describes
the spectral properties of the operators from this class. It may
happen that characteristic functions are simpler than the
corresponding operators; in this case one can significantly
simplify the problem under investigation for these operators. For
given characteristic function of an operator A, we construct, in
explicit form, an operator that serves as a model A of the operator
A in a certain linear space (to some extent this resembles the
construction of diagonal and triangular matrices' unitary
equivalent or similar, to certain matrix classes). The study of
this model operator may give much information about the original
operator (its spectrum, the completeness of the system of root
subspaces, etc.). In this book, we consider various classes of
linear (generally speaking, unbounded) operators, construct and
study their characteristic functions and models. We also present a
detailed study of contractiol)s and dissipative operators (in
particular, from the viewpoint of their triangulation).
General
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