Linear Operators: Spectral theory |
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Page 878
... corresponding to the function ƒ in C ( σ ( x ) ) under the * -isomorphism between B * ( x ) and C ( o ( x ) ) which is uniquely defined by the require- ment that x and g ( u ) = u be corresponding elements . The notation introduced in ...
... corresponding to the function ƒ in C ( σ ( x ) ) under the * -isomorphism between B * ( x ) and C ( o ( x ) ) which is uniquely defined by the require- ment that x and g ( u ) = u be corresponding elements . The notation introduced in ...
Page 942
... corresponding to λ is also an eigenfunction corresponding to λ . Thus every eigenfunction of T , which corresponds to a non - zero eigenvalue is a finite dimensional continuous function . Hence N is orthogonal to every eigenfunction ...
... corresponding to λ is also an eigenfunction corresponding to λ . Thus every eigenfunction of T , which corresponds to a non - zero eigenvalue is a finite dimensional continuous function . Hence N is orthogonal to every eigenfunction ...
Page 1780
... correspond- ing equivalence classes and that u EU . Consider an arbitrary ele- ment u in the basis { v } for which ( u , v ) ‡ 0 . It will be shown that υβ VE V. Since U and V are corresponding classes there are elements u , vg in U , V ...
... correspond- ing equivalence classes and that u EU . Consider an arbitrary ele- ment u in the basis { v } for which ( u , v ) ‡ 0 . It will be shown that υβ VE V. Since U and V are corresponding classes there are elements u , vg in U , V ...
Contents
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