Linear Operators, Part 2 |
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Page 1236
... set B ( x ) = 0 , i = 1 , ... , k , if the boundary values B are all linear combinations of the C ,. If each of two sets of boundary conditions is stronger than the other , then the sets are said to be equivalent . A set of boundary ...
... set B ( x ) = 0 , i = 1 , ... , k , if the boundary values B are all linear combinations of the C ,. If each of two sets of boundary conditions is stronger than the other , then the sets are said to be equivalent . A set of boundary ...
Page 1297
... boundary values " introduced in the last chapter . We shall see that the discussion leads us to a number of results ... set of boundary conditions B ( f ) = 0 , i 1 , . . . , k , is called stronger than a set C ; ( f ) = 0 , j 1 ...
... boundary values " introduced in the last chapter . We shall see that the discussion leads us to a number of results ... set of boundary conditions B ( f ) = 0 , i 1 , . . . , k , is called stronger than a set C ; ( f ) = 0 , j 1 ...
Page 1305
... boundary condition . A set of boundary conditions is said to be separated if it ( or , more generally , some set of boundary conditions equivalent to it ) contains no mixed boundary conditions . In all other cases the set is said to be a ...
... boundary condition . A set of boundary conditions is said to be separated if it ( or , more generally , some set of boundary conditions equivalent to it ) contains no mixed boundary conditions . In all other cases the set is said to be a ...
Contents
BAlgebras | 861 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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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 coefficients compact operator complex numbers constant continuous function converges Corollary deficiency indices Definition denote dense eigenvalues element equation essential spectrum Exercise exists finite dimensional follows from Lemma follows from Theorem follows immediately formal differential operator formally self adjoint formula Fourier function defined function f Hence Hilbert space Hilbert-Schmidt operator identity inequality integral interval isometric isomorphism kernel L₁ L₁(R L₂(I L₂(R Lemma Let f linear linearly independent mapping matrix measure neighborhood non-zero norm open set operators in Hilbert orthogonal orthonormal basis Plancherel's theorem positive preceding lemma prove real axis real numbers satisfies sequence solution spectral spectral theorem square-integrable subset subspace Suppose T₁ T₂ theory To(t topology unique unitary vanishes vector zero