Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
From inside the book
Results 1-3 of 68
Page 1280
... formal differential operator . If it is desired to emphasize the distinction between the case in which an 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 an is allowed to vanish and the opposite case , a formal differential operator may sometimes be referred to as a regular formal ...
Page 1290
... 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 operator , and let its leading coefficient be a ...
... 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 operator , and let its leading coefficient be a ...
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
IX | 859 |
Bounded Normal Operators in Hilbert Space | 887 |
Miscellaneous Applications | 937 |
Copyright | |
25 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 compact subset complex numbers continuous function converges Corollary deficiency indices Definition denote dense domain 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 isometric isomorphism kernel L₁(R L₂(I L₂(R Lemma Let f linear linearly independent mapping matrix measure neighborhood norm open set open subset orthonormal partial differential operator Plancherel's theorem positive PROOF prove real axis real numbers satisfies Section sequence solution spectral spectral theory square-integrable subspace Suppose T₁ T₁(t theory To(t topology unique unitary vanishes vector zero