Some Generalized Eigenfunction Expansions And Uniqueness Theorems
Some Generalized Eigenfunction Expansions And Uniqueness Theorems
Arthur S Peters
The book Some Generalized Eigenfunction Expansions And Uniqueness Theorems was written by author Arthur S Peters Here you can read free online of Some Generalized Eigenfunction Expansions And Uniqueness Theorems book, rate and share your impressions in comments. If you don't know what to write, just answer the question: Why is Some Generalized Eigenfunction Expansions And Uniqueness Theorems a good or bad book?
What reading level is Some Generalized Eigenfunction Expansions And Uniqueness Theorems book?
To quickly assess the difficulty of the text, read a short excerpt:
L8), as given by the authors noted above, depend upon explicit asymptotic estimates of the behavior of eigenfunctions and eigenvalues as A — »• 00 . For a proof of (2. 18) with respect to the second order system (2, 9)- (2. 11); and one which does not depend on specific asymptotic evalua- tions, see Peters [8]. The formula (2. L8) leads to the expansion of f(y) into an infinite sum of residues. If C is a circle with center at A^ containing no other eigenvalue we have 12 (2. 19) 00 -, r f(y) = -...) p^ r Q[G(t, y, z), f(t)] n=0 dz n 00 5 Q ^ 7^ G(t, y, z)clz, f(t) n If (X»(z) has a zero of order k at z = A, the corresponding term in the expansion (2. 19) is (2. 20) Q[?^(t, y, n), f(t)] where 9^(t, y, n)/(z ->^„) comes from the Laurent expansion of G(t, y, z) for the neighborhood of z = A . The function 9 can be obtained by substituting the expansion 00 G(t, y, z) = y— (z - A^)* 0_^(t, y, n) + T~ [z - A^)* 9^(t, y, n) in the equation LG(t, y, z) -A^r(t)G - (z -A^)rG = 5(t - y) and the boundary conditions G^(0, y, z) +PQG(0, y, z) = a^A^G(0, y, z) + a^(z - A^)G(0, y, z), G^(l, y, z) + p^G(l, y, z) = a^A^G(l, y, z) + a^(z -A^)G(l, y, z) which define G(t, y, z).
User Reviews: