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 e2 , then the second order equation L'f ' = 0 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 e2 , then the second order equation L'f ' = 0 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 |
Bounded Normal Operators in Hilbert Space | 887 |
Miscellaneous Applications | 937 |
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adjoint extension adjoint operator algebra analytic B-algebra B*-algebra Borel set boundary conditions boundary values bounded operator C₁ closed closure Co(I coefficients complex numbers converges Corollary deficiency indices Definition denote dense domain eigenfunctions eigenvalues element essential spectrum 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 kernel L₁(R L₂(I L₂(R Lemma Let f linearly independent mapping Math matrix measure neighborhood norm open set operators in Hilbert orthogonal orthonormal partial differential operator Plancherel's theorem positive preceding lemma prove real axis real numbers representation satisfies Section sequence solution spectral spectral theory square-integrable subspace Suppose symmetric operator T₁ T₂ theory To(t topology unique unitary vanishes vector zero