Linear Operators: Spectral theory |
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Page 1162
... regular maximal ideals of L ( R ) are in one - to - one correspondence with the points of Mo , i.e. , with all the maximal ideals of the algebra obtained by adjoining an identity to L1 ( R ) except the point at infinity of M. Now in an ...
... regular maximal ideals of L ( R ) are in one - to - one correspondence with the points of Mo , i.e. , with all the maximal ideals of the algebra obtained by adjoining an identity to L1 ( R ) except the point at infinity of M. Now in an ...
Page 1505
... regular singular point at which the exponents are zero and one . If Lf = 0 is a differential equation with rational coefficients and a regular singularity z with exponents e1 and e2 , then the second order equation L'f ' = = 0 satisfied ...
... regular singular point at which the exponents are zero and one . If Lf = 0 is a differential equation with rational coefficients and a regular singularity z with exponents e1 and e2 , then the second order equation L'f ' = = 0 satisfied ...
Page 1917
... Regular closure , ( 462-463 ) Regular convexity , ( 462-463 ) Regular element in a B - algebra , IX.1.2 ( 861 ) Regular element in a ring , ( 40 ) Regular method of summability , II.4.35 ( 75 ) Regular point of a differential equa- tion ...
... Regular closure , ( 462-463 ) Regular convexity , ( 462-463 ) Regular element in a B - algebra , IX.1.2 ( 861 ) Regular element in a ring , ( 40 ) Regular method of summability , II.4.35 ( 75 ) Regular point of a differential equa- tion ...
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 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 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