Linear Operators, Part 2 |
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Page 1217
... respectively , with measures u and μ , and multiplicity sets { e } and { e } will be called equivalent if u μ and μ ( e „ „ ) = 0 = μ ( e̟ „ Дễn ) for n = 1 , 2 , .... 16 THEOREM . A separable Hilbert space $ has an ordered ...
... respectively , with measures u and μ , and multiplicity sets { e } and { e } will be called equivalent if u μ and μ ( e „ „ ) = 0 = μ ( e̟ „ Дễn ) for n = 1 , 2 , .... 16 THEOREM . A separable Hilbert space $ has an ordered ...
Page 1548
... respectively by the boundary conditions f ( c ) = ƒ ' ( c ) = f ( n - 1 ) ( c ) = 0 and by the boundary conditions in the set B at the right and at the left endpoints of I respectively . Show that the operators T1 and T2 are self ...
... respectively by the boundary conditions f ( c ) = ƒ ' ( c ) = f ( n - 1 ) ( c ) = 0 and by the boundary conditions in the set B at the right and at the left endpoints of I respectively . Show that the operators T1 and T2 are self ...
Page 1736
... respectively , having carriers , respectively , equal to the carriers of f and g , and that we then have ( 4 ) ( % + K ) ƒ € + teĴ € = ĝe⋅ τ Moreover , by Lemma 3.24 ( as generalized to D ,, ( C ) ) , fe is in Ho ( C ) . It is clear ...
... respectively , having carriers , respectively , equal to the carriers of f and g , and that we then have ( 4 ) ( % + K ) ƒ € + teĴ € = ĝe⋅ τ Moreover , by Lemma 3.24 ( as generalized to D ,, ( C ) ) , fe is in Ho ( C ) . It is clear ...
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 domain 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 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 tr(T transform unique unitary vanishes vector zero