Linear Operators, Part 2 |
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Page 1505
... order l at 50 , then the second order equation L " f " 0 satisfied by f " = f [ p ( x ) ] has rational coefficients also . The operator L ' has a regular sin- gularity at 。 with exponents le1 , le . = By passing from the equation Lf ...
... order l at 50 , then the second order equation L " f " 0 satisfied by f " = f [ p ( x ) ] has rational coefficients also . The operator L ' has a regular sin- gularity at 。 with exponents le1 , le . = By passing from the equation Lf ...
Page 1816
... second order . Duke Math . J. 14 , 323-326 ( 1947 ) . Unrestricted solution fields of almost separable differential equations . Trans . Amer . Math . Soc . 63 , 560-580 ( 1948 ) . On differential equations with non - oscillatory ...
... second order . Duke Math . J. 14 , 323-326 ( 1947 ) . Unrestricted solution fields of almost separable differential equations . Trans . Amer . Math . Soc . 63 , 560-580 ( 1948 ) . On differential equations with non - oscillatory ...
Page 1834
... second order linear differential equation . Duke Math . J. 17 , 57-62 ( 1950 ) . On self - adjoint differential equations of second order . J. London Math . Soc . 27 , 33-47 ( 1952 ) . Sur la notion du groupe abstrait topologique . Fund ...
... second order linear differential equation . Duke Math . J. 17 , 57-62 ( 1950 ) . On self - adjoint differential equations of second order . J. London Math . Soc . 27 , 33-47 ( 1952 ) . Sur la notion du groupe abstrait topologique . Fund ...
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