Linear Operators: Spectral operators |
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Page 1236
boundary conditions C,(r) = 0, j = 1,..., m, is said to be stronger than the set B,(r) =
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 ...
boundary conditions C,(r) = 0, j = 1,..., m, is said to be stronger than the set B,(r) =
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 ...
Page 1305
If B(f) = 0 is not a boundary condition either at a or at b (so that, by Theorem 19,
the equation B(f) = 0 may be written as B1 (f) = B.(f), where B, and B, are non-zero
boundary values at a and b respectively), then B(f) = 0 is said to be a mired ...
If B(f) = 0 is not a boundary condition either at a or at b (so that, by Theorem 19,
the equation B(f) = 0 may be written as B1 (f) = B.(f), where B, and B, are non-zero
boundary values at a and b respectively), then B(f) = 0 is said to be a mired ...
Page 1310
imposition of a separated symmetric set of boundary conditions. Let Jož # 0. Then
the boundary conditions are real, and there is eractly one solution p(t, 2) of (t–%)
p = 0 square-integrable at a and satisfying the boundary conditions at a, and ...
imposition of a separated symmetric set of boundary conditions. Let Jož # 0. Then
the boundary conditions are real, and there is eractly one solution p(t, 2) of (t–%)
p = 0 square-integrable at a and satisfying the boundary conditions at a, and ...
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Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
4 Exercises | 879 |
Copyright | |
52 other sections not shown
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Linear Operators, Part 1 Nelson Dunford,Jacob T. Schwartz,William G. Bade,Robert G. Bartle Snippet view - 1958 |
Common terms and phrases
adjoint extension adjoint operator algebra analytic B-algebra B-space Borel set boundary conditions boundary values bounded operator closed closure Cº(I coefficients compact operator complex numbers constant continuous function converges Corollary deficiency indices Definition denote dense domain eigenfunctions 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 infinity integral interval kernel Lemma Let f Let Q 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 numbers satisfies sequence singular ſº solution spectral spectral theorem square-integrable subspace Suppose symmetric operator theory To(r To(t topology transform uniformly unique unitary vanishes vector zero