Author | Gorbachuk, M. L. author |
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Title | M.G. Krein's Lectures on Entire Operators [electronic resource] / by M. L. Gorbachuk, V. I. Gorbachuk |
Imprint | Basel : Birkhรคuser Basel : Imprint: Birkhรคuser, 1997 |
Connect to | http://dx.doi.org/10.1007/978-3-0348-8902-5 |
Descript | IX, 222 p. online resource |
1 Some aspects of operator theory and the theory of analytic functions -- 1 On spectral functions of Hermitian operators -- 2. Representation of a simple Hermitian operator whose deficiency index is (1,1) -- 3. On the spectrum of self-adjoint extensions of a Hermitian operator whose deficiency index is (1,1) -- 4. Some aspects of the theory of analytic functions -- 2 Entire operators whose deficiency index is (1,1) -- 1. Quasiregular gauge -- 2. Principal theorem on regular points of fM(z) -- 3. u -regular points of a Hermitian operator -- 4. Functions e(z) and ?M(Z) -- 5. Entire operators -- 6. R-functions and generalized resolvents of a Hermitian operator -- 7. On distribution functions of a Hermitian operator -- 8. Method of directing functionals -- 9. Operator, entire with respect to a generalized gauge -- 3 Applications of entire operator theory to some classical problems of analysis -- 1. Power moment problem -- 2. Continuation problem for positive definite functions -- 3. Unitary and spiral curves -- Appendix 1 On entire operators whose defect numbers are arbitrary -- Appendix 2 Enture operators represented by differential operators -- Appendix 3 On a difficult problem of operator theory and its relation to classical analysis -- Comments