Linear Operators, Part 2 |
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Page 1310
... solution y of ( 7-2 ) y = 0 square - integrable at b and satisfying all boundary conditions at b , and at least one solution of ( 7-2 ) = 0 square - integrable at a and satisfying all the boundary conditions at a . Suppose there were a ...
... solution y of ( 7-2 ) y = 0 square - integrable at b and satisfying all boundary conditions at b , and at least one solution of ( 7-2 ) = 0 square - integrable at a and satisfying all the boundary conditions at a . Suppose there were a ...
Page 1464
... solution of the equation -f " at - 2f O has an infinite number of zeros , and that for a > − ( 1/4 ) , no solution , not identically zero , does . Now , two solutions of −ƒ ' ' + at ̄2f = 0 are te and tea , where e1 , e2 1 / 2 + Va + ...
... solution of the equation -f " at - 2f O has an infinite number of zeros , and that for a > − ( 1/4 ) , no solution , not identically zero , does . Now , two solutions of −ƒ ' ' + at ̄2f = 0 are te and tea , where e1 , e2 1 / 2 + Va + ...
Page 1529
... solution whose asymp- totic expansion begins with the factor exp ( ¿ 1 ) 2−1 ) . Thus , a solution ( " small solution " ) with the first kind of asymptotic expansion is uniquely determined by its asymptotic expansion ; while a solution ...
... solution whose asymp- totic expansion begins with the factor exp ( ¿ 1 ) 2−1 ) . Thus , a solution ( " small solution " ) with the first kind of asymptotic expansion is uniquely determined by its asymptotic expansion ; while a solution ...
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 domain 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 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 open set operators in Hilbert orthogonal orthonormal basis Plancherel's theorem positive preceding lemma 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