Linear Operators: Spectral theory |
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Page 1904
... set functions , III.7.2-4 ( 158–160 ) , IV.8.8 ( 292 ) , IV.9.4-5 ( 308 ) , IV.9.15 ( 316 ) , IV.10.6 ( 321 ) , IV ... Convex combination , V.2.2 ( 414 ) . ( See also Convex hull , Convex set , Convex space ) Convex function , definition ...
... set functions , III.7.2-4 ( 158–160 ) , IV.8.8 ( 292 ) , IV.9.4-5 ( 308 ) , IV.9.15 ( 316 ) , IV.10.6 ( 321 ) , IV ... Convex combination , V.2.2 ( 414 ) . ( See also Convex hull , Convex set , Convex space ) Convex function , definition ...
Page 1911
... set , I.4.1 ( 10 ) Internal point , definition , V.1.6 ( 410 ) Intervals , definitions , ( 4 ) , III.5.15 ( 140 ) ... convex closure of a weakly compact set , V.6.4 ( 434 ) on X closed convex sets in X * , V.5.7 ( 429 ) L Lacunary series ...
... set , I.4.1 ( 10 ) Internal point , definition , V.1.6 ( 410 ) Intervals , definitions , ( 4 ) , III.5.15 ( 140 ) ... convex closure of a weakly compact set , V.6.4 ( 434 ) on X closed convex sets in X * , V.5.7 ( 429 ) L Lacunary series ...
Page 1912
... set or se- quence of real numbers , ( 4 ) of a sequence of sets , III.4.3 ( 126 ) point of a set , I.4.1 ( 10 ) weak ... convex space , definition , V.2.9 ( 417 ) local convexity , of land weak topol- ogies , V.3.3 ( 419 ) of * in the bounded ...
... set or se- quence of real numbers , ( 4 ) of a sequence of sets , III.4.3 ( 126 ) point of a set , I.4.1 ( 10 ) weak ... convex space , definition , V.2.9 ( 417 ) local convexity , of land weak topol- ogies , V.3.3 ( 419 ) of * in the bounded ...
Contents
BAlgebras | 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 complex numbers converges Corollary deficiency indices Definition denote dense 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 defined function f Haar measure Hence Hilbert space Hilbert-Schmidt operator identity inequality integral interval kernel L₁(R L₂(I L₂(R Lemma Let f linearly independent mapping Math matrix measure neighborhood norm open set operators in Hilbert orthogonal orthonormal partial differential operator Plancherel's theorem positive preceding lemma prove real axis real numbers representation satisfies Section sequence solution spectral spectral theory square-integrable subspace Suppose symmetric operator T₁ T₂ theory To(t topology unique unitary vanishes vector zero