Linear Operators: Spectral operators |
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Page 1272
... indices are d1 = 0 , d_ = 1 . The operator T1 is called an elementary symmetric operator . It may be proved that if T is maximal symmetric with indices d 0 , d_ n ( where n is any cardinal number ) , then may be broken into a direct sum ...
... indices are d1 = 0 , d_ = 1 . The operator T1 is called an elementary symmetric operator . It may be proved that if T is maximal symmetric with indices d 0 , d_ n ( where n is any cardinal number ) , then may be broken into a direct sum ...
Page 1398
... indices of To ( T ) is k , then for λo , ( T ) the equation to ho has at least λσ k linearly independent solutions in L¿ ( I ) . PROOF . By Theorem 2.10 and XII.4.7 ( c ) , the adjoint of To ( 7 ) is T1 ( 7 ) . The desired result thus ...
... indices of To ( T ) is k , then for λo , ( T ) the equation to ho has at least λσ k linearly independent solutions in L¿ ( I ) . PROOF . By Theorem 2.10 and XII.4.7 ( c ) , the adjoint of To ( 7 ) is T1 ( 7 ) . The desired result thus ...
Page 1610
... indices of t are equal and that there exists a sequence { f } of square - integrable functions such that f vanishes ... indices and boundary values . Since every estimation of the number of deficiency indices immediately yields an ...
... indices of t are equal and that there exists a sequence { f } of square - integrable functions such that f vanishes ... indices and boundary values . Since every estimation of the number of deficiency indices immediately yields an ...
Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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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 Haar measure 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 operators in Hilbert orthogonal orthonormal basis Plancherel's theorem positive preceding lemma PROOF prove real axis satisfies sequence solution spectral spectral theorem square-integrable subset subspace Suppose T₁ T₁(t T₂ theory To(t topology unique unitary vanishes vector zero