Linear Operators: Spectral theory |
From inside the book
Results 1-3 of 66
Page 1280
... formal differential operator . If it is desired to emphasize the distinction between the case in which a is allowed to vanish and the opposite case , a formal differential operator may sometimes be referred to as a regular formal ...
... formal differential operator . If it is desired to emphasize the distinction between the case in which a is allowed to vanish and the opposite case , a formal differential operator may sometimes be referred to as a regular formal ...
Page 1290
... formally self adjoint provided that p ( t ) is a real function . If we use these observations inductively , we can give a closed form for the most general formally symmetric formal differential operator of order n . Indeed , let be such an ...
... formally self adjoint provided that p ( t ) is a real function . If we use these observations inductively , we can give a closed form for the most general formally symmetric formal differential operator of order n . Indeed , let be such an ...
Page 1540
... formal differential operator on an interval I , and let B be a compact operator in L2 ( I ) . Prove that the essential spectrum of 7 coincides with the essential spectrum of the operator T1 ( 7 ) + B . All Let be a regular formal ...
... formal differential operator on an interval I , and let B be a compact operator in L2 ( I ) . Prove that the essential spectrum of 7 coincides with the essential spectrum of the operator T1 ( 7 ) + B . All Let be a regular formal ...
Contents
BAlgebras | 859 |
Bounded Normal Operators in Hilbert Space | 887 |
Miscellaneous Applications | 937 |
Copyright | |
37 other sections not shown
Other editions - View all
Common terms and phrases
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