Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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Page 1629
... partial differential operators . Since the theory of linear partial differential operators is vast and highly ramified , we shall only touch upon a number of its aspects , with the intention of displaying a bouquet of applications of ...
... partial differential operators . Since the theory of linear partial differential operators is vast and highly ramified , we shall only touch upon a number of its aspects , with the intention of displaying a bouquet of applications of ...
Page 1703
... partial differential operators ? In the present section it will be seen that it can , at least for the class of elliptic partial differential operators to be defined below . A crucial theorem in the development of the theory of Chapter ...
... partial differential operators ? In the present section it will be seen that it can , at least for the class of elliptic partial differential operators to be defined below . A crucial theorem in the development of the theory of Chapter ...
Page 1705
... partial differential operator of order at most p - 1 . τεφ satisfies the It follows from ( 1 ) , from Lemmas 3.22 , 3.18 and 3.6 ( iv ) , and on placing ( fo S1 ) = fg , that the distribution f partial differential equation ( 2 ) Σ a ̧ ...
... partial differential operator of order at most p - 1 . τεφ satisfies the It follows from ( 1 ) , from Lemmas 3.22 , 3.18 and 3.6 ( iv ) , and on placing ( fo S1 ) = fg , that the distribution f partial differential equation ( 2 ) Σ a ̧ ...
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