Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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Page 1278
... operator is by no means trivial ; the study of symmetric unbounded operators in Section XII.4 indicates that for unbounded operators , the ... Differential Operators Introduction: Elementary Properties of Formal Differential Operators •
... operator is by no means trivial ; the study of symmetric unbounded operators in Section XII.4 indicates that for unbounded operators , the ... Differential Operators Introduction: Elementary Properties of Formal Differential Operators •
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
... 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 ...
Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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Acad adjoint extension adjoint operator algebra Amer analytic B-algebra B*-algebra Banach Banach spaces Borel set boundary conditions boundary values bounded operator C₁ closed closure Co(I coefficients complex numbers continuous function converges Corollary deficiency indices Definition denote dense differential equations Doklady Akad domain eigenfunctions eigenvalues element essential spectrum exists follows from Lemma follows immediately formal differential operator formally self adjoint formula 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 linearly independent mapping Math matrix measure Nauk SSSR N. S. neighborhood norm open set operators in Hilbert orthogonal orthonormal positive Proc PROOF prove real axis satisfies sequence singular solution spectral spectral theory square-integrable subspace Suppose T₁ T₂ theory To(t topology transform unique unitary vanishes vector zero