Linear Operators: Spectral theory |
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Page 856
... Theory : General Case 1333 6. Qualitative Theory of the Deficiency Index . · 1392 7. Qualitative Theory of the Spectrum • 1435 8. Examples . 1503 9. Exercises . 1538 10. Notes and Remarks 1581 XIV . Linear Partial Differential Equations ...
... Theory : General Case 1333 6. Qualitative Theory of the Deficiency Index . · 1392 7. Qualitative Theory of the Spectrum • 1435 8. Examples . 1503 9. Exercises . 1538 10. Notes and Remarks 1581 XIV . Linear Partial Differential Equations ...
Page 1645
... theory of generalized functions was given by Laurent Schwartz ; the generalized functions were called by him " distributions . " It is the purpose of the present section to develop ... THEORY OF DISTRIBUTIONS The Theory of Distributions 1629.
... theory of generalized functions was given by Laurent Schwartz ; the generalized functions were called by him " distributions . " It is the purpose of the present section to develop ... THEORY OF DISTRIBUTIONS The Theory of Distributions 1629.
Page 1882
... theory of linear nonselfadjoint operators . Doklady Akad . Nauk SSSR 130 , 254-256 ( 1960 ) . 21. On spectrally complete systems of generalized eigenvectors of a dissipative operator . Uspekhi Math . Nauk . 14 , 145–152 ( 1959 ) ...
... theory of linear nonselfadjoint operators . Doklady Akad . Nauk SSSR 130 , 254-256 ( 1960 ) . 21. On spectrally complete systems of generalized eigenvectors of a dissipative operator . Uspekhi Math . Nauk . 14 , 145–152 ( 1959 ) ...
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