Linear Operators: Spectral theory |
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Page 1279
^3 In this whole chapter, the letter / will denote an interval of the ag real axis. The
interval / can be open, half-open, or closed. The interval ^! [a, oo ) is considered
to be half-open; the interval ( — oo, + oo) to be 25j open. Thus a closed interval ...
^3 In this whole chapter, the letter / will denote an interval of the ag real axis. The
interval / can be open, half-open, or closed. The interval ^! [a, oo ) is considered
to be half-open; the interval ( — oo, + oo) to be 25j open. Thus a closed interval ...
Page 1597
(18) In the interval [0, oo), suppose that (a) lim q(t) = — oo, (-.CO (b) lim sup \ < co
, <~o° \q(t)\3 c )* v ' dt < 00, for large M. Then the essential spectrum of r is empty (
Wintner [8] ). (19) In the interval [a, co), suppose that lim q(t) = c. (-i> Then the ...
(18) In the interval [0, oo), suppose that (a) lim q(t) = — oo, (-.CO (b) lim sup \ < co
, <~o° \q(t)\3 c )* v ' dt < 00, for large M. Then the essential spectrum of r is empty (
Wintner [8] ). (19) In the interval [a, co), suppose that lim q(t) = c. (-i> Then the ...
Page 1599
(30) In the interval (0,6] assume that as t -*□ 0, 1 1 q(t) H 1 ->• oo, HK ' 4<2 4t*
log2 1 then the essential spectrum of r is void (Berkowitz [1]). Other conditions
which allow the approximate determination of the essential spectrum are the ...
(30) In the interval (0,6] assume that as t -*□ 0, 1 1 q(t) H 1 ->• oo, HK ' 4<2 4t*
log2 1 then the essential spectrum of r is void (Berkowitz [1]). Other conditions
which allow the approximate determination of the essential spectrum are the ...
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Contents
BAlgebras | 859 |
Bounded Normal Operators in Hilbert Space | 887 |
Miscellaneous Applications | 937 |
Copyright | |
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Acad adjoint extension adjoint operator algebra Amer analytic B*-algebra Banach spaces Borel set boundary conditions boundary values bounded operator closed closure coefficients complex numbers constant continuous function converges Corollary deficiency indices Definition denote dense differential equations Doklady Akad domain eigenfunctions eigenvalues element essential spectrum exists finite dimensional follows from Lemma follows from Theorem follows immediately formal differential operator formally self adjoint formula Fourier function q Haar measure Hence Hilbert space Hilbert-Schmidt operator hypothesis identity inequality integral interval kernel Lemma linear operator linearly independent mapping matrix measure Nauk SSSR N. S. neighborhood norm open set operators in Hilbert orthogonal orthonormal partial differential operator Plancherel's theorem positive preceding lemma Proc prove real axis real numbers representation satisfies Section sequence singular solution spectral spectral theory square-integrable subspace Suppose symmetric operator theory topology transform unique unitary vanishes vector zero