Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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Page 1378
... preceding theorem . Moreover , in the course of the proof preceding the statement of Theorem 23 , it was shown that if 2 is any point in △ , there exists a small open subinterval N of 4 , containing 2 , such that the set of ...
... preceding theorem . Moreover , in the course of the proof preceding the statement of Theorem 23 , it was shown that if 2 is any point in △ , there exists a small open subinterval N of 4 , containing 2 , such that the set of ...
Page 1419
... preceding lemma , f ( t ) ≤ fi ( t ) in [ 8 + 1 , mi + 1 ] . In particular − f ( mi + 1 ) = \ f ( m¡ + 1 ) ¦ ≤ f1 ... preceding corollary . Q.E.D. PROOF OF THEOREM 24. If the function q of Theorem 24 is not negative for t sufficiently ...
... preceding lemma , f ( t ) ≤ fi ( t ) in [ 8 + 1 , mi + 1 ] . In particular − f ( mi + 1 ) = \ f ( m¡ + 1 ) ¦ ≤ f1 ... preceding corollary . Q.E.D. PROOF OF THEOREM 24. If the function q of Theorem 24 is not negative for t sufficiently ...
Page 1771
... preceding theorem and Theorem 6.23 . Statement ( ii ) follows from statement ( ii ) of the preceding theorem , since a function satisfying the hypotheses of the present statement ( ii ) evidently ( cf. Theorem 6.23 ) satisfies the ...
... preceding theorem and Theorem 6.23 . Statement ( ii ) follows from statement ( ii ) of the preceding theorem , since a function satisfying the hypotheses of the present statement ( ii ) evidently ( cf. Theorem 6.23 ) satisfies the ...
Contents
IX | 859 |
Bounded Normal Operators in Hilbert Space | 887 |
Miscellaneous Applications | 937 |
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adjoint extension adjoint operator algebra analytic B-algebra B*-algebra Borel set boundary conditions boundary values bounded operator C₁ closed closure Co(I coefficients compact subset complex numbers continuous function converges Corollary deficiency indices Definition denote dense domain eigenvalues element essential spectrum exists finite dimensional follows from Lemma follows from Theorem follows immediately formal differential operator formally self adjoint formula Fourier function defined function f Haar measure Hence Hilbert space Hilbert-Schmidt operator identity inequality integral interval isometric isomorphism kernel L₁(R L₂(I L₂(R Lemma Let f linear linearly independent mapping matrix measure neighborhood norm open set open subset orthonormal partial differential operator Plancherel's theorem positive PROOF prove real axis real numbers satisfies Section sequence solution spectral spectral theory square-integrable subspace Suppose T₁ T₁(t theory To(t topology unique unitary vanishes vector zero