Linear Operators: Spectral theory |
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Page 1815
... space and the theory of spectral multiplicity . Chelsea , New York , 1951 . Finite dimensional vector spaces . Ann . of Math . Stud . No. 7. Princeton Univ . Press , Princeton , 1942 . An ergodic theorem . Proc . Nat . Acad . Sci ...
... space and the theory of spectral multiplicity . Chelsea , New York , 1951 . Finite dimensional vector spaces . Ann . of Math . Stud . No. 7. Princeton Univ . Press , Princeton , 1942 . An ergodic theorem . Proc . Nat . Acad . Sci ...
Page 1903
... space , definition , I.6.5 ( 19 ) compact , properties , I.6.7 ( 20 ) , I.6.9 ( 20 ) Complete normed linear space . ( See B - space ) Complete orthonormal set , in Hilbert space , IV.4.8 ( 250 ) Complete partially ordered space , def ...
... space , definition , I.6.5 ( 19 ) compact , properties , I.6.7 ( 20 ) , I.6.9 ( 20 ) Complete normed linear space . ( See B - space ) Complete orthonormal set , in Hilbert space , IV.4.8 ( 250 ) Complete partially ordered space , def ...
Page 1922
... spaces , I.8.5 ( 32 ) U Ultrafilter , definition , I.7.10 ( 30 ) properties , I.7.11-12 ( 30 ) Unbounded operators , exercises on , VII.10 in Hilbert space , Chap . XII remarks on , ( 612 ) study of , VII.9 Unconditional convergence of ...
... spaces , I.8.5 ( 32 ) U Ultrafilter , definition , I.7.10 ( 30 ) properties , I.7.11-12 ( 30 ) Unbounded operators , exercises on , VII.10 in Hilbert space , Chap . XII remarks on , ( 612 ) study of , VII.9 Unconditional convergence of ...
Contents
SPECTRAL THEORY Self Adjoint Operators in Hilbert Space | 858 |
BAlgebras | 859 |
Commutative BAlgebras | 868 |
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A₁ adjoint extension adjoint operator algebra analytic B-algebra Borel set boundary conditions boundary values bounded operator C₁ closed closure coefficients compact operator complex numbers continuous function converges Corollary deficiency indices Definition denote dense eigenvalues element equation essential spectrum Exercise exists finite dimensional follows from Lemma follows from Theorem follows immediately formal differential operator formally self adjoint formula Fourier function defined function f Hence Hilbert space Hilbert-Schmidt operator identity inequality integral interval isometric isomorphism kernel L₁ L₁(R L₂(I L₂(R Lemma Let f linear linearly independent mapping matrix measure neighborhood non-zero norm open set operators in Hilbert orthogonal orthonormal basis Plancherel's theorem positive preceding lemma prove real axis real numbers satisfies sequence solution spectral spectral theorem square-integrable subspace Suppose T₁ T₂ theory To(t topology transform unique unitary vanishes vector zero