Linear Operators: Spectral theory |
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Page 1505
... equation L " f " = 0 satisfied by f " = f [ p ( ) ] has rational coefficients also . The operator L " has a regular sin- gularity at So with exponents le1 , le . = By passing from the equation Lf 0 to the equation L " " " " = 0 ...
... equation L " f " = 0 satisfied by f " = f [ p ( ) ] has rational coefficients also . The operator L " has a regular sin- gularity at So with exponents le1 , le . = By passing from the equation Lf 0 to the equation L " " " " = 0 ...
Page 1529
... equation has the characteristic equation x2 - α = 0 , so that ( 1 ) = 0 , 1 ) 1. Thus the Stokes lines for this equation are the positive and negative imaginary axes . Trying solutions of the form z - 1 ( 1 + c / z + ... ) and ez - 2 ...
... equation has the characteristic equation x2 - α = 0 , so that ( 1 ) = 0 , 1 ) 1. Thus the Stokes lines for this equation are the positive and negative imaginary axes . Trying solutions of the form z - 1 ( 1 + c / z + ... ) and ez - 2 ...
Page 1553
... equation ( 2-7 ) = 0 is bounded . Prove that 7 has no boundary values at infinity . G4 ( Wintner ) Suppose that the ... equation ( 2-7 ) 0. Prove : = ( a ) either f is square - integrable , or the point 2 belongs to the essential ...
... equation ( 2-7 ) = 0 is bounded . Prove that 7 has no boundary values at infinity . G4 ( Wintner ) Suppose that the ... equation ( 2-7 ) 0. Prove : = ( a ) either f is square - integrable , or the point 2 belongs to the essential ...
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