Linear Operators: Spectral theory |
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Page 849
Nelson Dunford, Jacob T. Schwartz. PURE AND APPLIED MATHEMATICS A Series of Texts and Monographs Edited by : R. COURANT Vol . I : Vol . II : Vol . III : L. BERS J. J. STOKER Supersonic ... APPLIED MATHEMATICS A Series of Texts and Monographs.
Nelson Dunford, Jacob T. Schwartz. PURE AND APPLIED MATHEMATICS A Series of Texts and Monographs Edited by : R. COURANT Vol . I : Vol . II : Vol . III : L. BERS J. J. STOKER Supersonic ... APPLIED MATHEMATICS A Series of Texts and Monographs.
Page 945
... applied in an interesting and significant manner to the analysis of the space AP of almost periodic functions on the real line R = ( -∞ , ∞ ) . In fact , the theory will be applied in this section to prove the principal result in H ...
... applied in an interesting and significant manner to the analysis of the space AP of almost periodic functions on the real line R = ( -∞ , ∞ ) . In fact , the theory will be applied in this section to prove the principal result in H ...
Page 1278
... applied " to a function f , if , say , f belongs to C " . Thus , we can define an operator whose domain is C " ( but whose range is not in C " , only in C ) . We might , however , have " applied " the formal differential operator to a ...
... applied " to a function f , if , say , f belongs to C " . Thus , we can define an operator whose domain is C " ( but whose range is not in C " , only in C ) . We might , however , have " applied " the formal differential operator to a ...
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