Linear Operators: Spectral theory |
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Page 1162
... regular maximal ideals of L1 ( 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 L1 ( 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 e , and e , then the second order equation L'f ' O satisfied by ...
... 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 e , and e , then the second order equation L'f ' O satisfied by ...
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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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