Linear Operators: Spectral theory |
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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 1289
... formal algebra of formal differential operators are worth mentioning although we shall not make much use of them ; for this reason they will not be numbered as theorems and lemmas . They will be valid for both regular and irregular formal ...
... formal algebra of formal differential operators are worth mentioning although we shall not make much use of them ; for this reason they will not be numbered as theorems and lemmas . They will be valid for both regular and irregular formal ...
Page 1290
... formal differential operator ( i / 2 ) ( d / dt ) " { p ( t ) ( d / dt ) + ( d / dt ) p ( t ) } ( d / dt ) " is formally self adjoint provided that p ( t ) is a real function . If we use these observations inductively , we can give a ...
... formal differential operator ( i / 2 ) ( d / dt ) " { p ( t ) ( d / dt ) + ( d / dt ) p ( t ) } ( d / dt ) " is formally self adjoint provided that p ( t ) is a real function . If we use these observations inductively , we can give a ...
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