Linear Operators: Spectral theory |
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Results 1-3 of 18
Page 1899
... weakly compact operator , VI.4.7-8 ( 484-485 ) Adjoint space , definition , II.3.7 ( 61 ) representation for special spaces , IV.15 a.e. ( See Almost everywhere ) Affine mapping , definition , ( 456 ) fixed points of , V.10.6 ( 456 ) ...
... weakly compact operator , VI.4.7-8 ( 484-485 ) Adjoint space , definition , II.3.7 ( 61 ) representation for special spaces , IV.15 a.e. ( See Almost everywhere ) Affine mapping , definition , ( 456 ) fixed points of , V.10.6 ( 456 ) ...
Page 1915
... weakly compact , definition , VI.4.1 ( 482 ) study of , VI.4 zero , ( 37 ) Operator topologies , VI.1 bounded strong , VI.9.9 ( 512 ) bounded weak , VI.9.7-10 ( 512 ) continuous linear functionals in , VI.1.4 ( 477 ) properties , VI.9.1 ...
... weakly compact , definition , VI.4.1 ( 482 ) study of , VI.4 zero , ( 37 ) Operator topologies , VI.1 bounded strong , VI.9.9 ( 512 ) bounded weak , VI.9.7-10 ( 512 ) continuous linear functionals in , VI.1.4 ( 477 ) properties , VI.9.1 ...
Page 1923
... Weak Cauchy sequence , criteria for in special spaces , IV.15 definition , II.3.25 ( 67 ) Weak completeness ... Weakly compact operator , in C , VI.7.1 ( 490 ) , VI.7.3–6 ( 493–496 ) definition , VI.4.1 ( 482 ) in L1 , VI.8.1 ...
... Weak Cauchy sequence , criteria for in special spaces , IV.15 definition , II.3.25 ( 67 ) Weak completeness ... Weakly compact operator , in C , VI.7.1 ( 490 ) , VI.7.3–6 ( 493–496 ) definition , VI.4.1 ( 482 ) in L1 , VI.8.1 ...
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BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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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 countably deficiency indices Definition denote dense eigenfunctions eigenvalues element equation essential spectrum Exercise exists f₁ finite dimensional follows from Lemma follows from Theorem formal differential operator formally self adjoint formula Fourier function f Haar measure Hence Hilbert space Hilbert-Schmidt operator homomorphism identity inequality infinity integral interval kernel L₁ L₁(R L₂ L₂(I L₂(R Lemma Let f linearly independent mapping matrix measure neighborhood non-zero norm operators in Hilbert orthogonal Plancherel's theorem positive preceding lemma prove real axis real numbers satisfies sequence shows solution spectral set spectral theorem square-integrable subset subspace Suppose T₁ T₂ theory To(t topology tr(T transform uniformly unique unitary vanishes vector zero