Linear Ordinary Differential Operators of the Second Order
Linear Ordinary Differential Operators of the Second Order
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In our eReader you can find the full English version of the book. Read Linear Ordinary Differential Operators of the Second Order Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book Linear Ordinary Differential Operators of the Second Order
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L) (tlif. T is, in D), This incidentally, proves that R(X, L) satisfies Eq. (13). Finally we note that the conditions of the theorem are satisfied by the functions y such that y(0) = and y, y', and y*' are absolutely continuous and all vanish outside a finite inter- val. Hence these functions lie in D; and since they are dense in 1^(0, oo) then by our definition L is a well-defined operator, Theorez: 2. 2 . The resolvent E(X, L) exists for all Im(X) > and is given in the Tisual way by (11).
It ...is clear that if the range of R(\, L) is contained in D then (2) will be satisfied. Let f e 1^(0, 00) and set y = R(X, L)f in Eq. (11). It is again clear that y, y* are absolutely continuous, that y and -y^' + q(x)y belong to 12(0, 00), and that y(0) = 0. Finally -9- V^ [y. H;(x, X^) ] = W^[v(x, \), v(x, \^) ] r ()(y. X) f(y) dy -'o + W^ |^()(x, X), v(x, \q) J [ vt/(y. X) f(y) dy.
z Now in the limit circle case toth f (J(yiX) f (y) dy — ^ limit and 7 v(yiX) f (y) dy —4 0. We now make use of two results due to Titchmarsh [5] (d 22 V namely, (16) .
What to read after Linear Ordinary Differential Operators of the Second Order?
You can find similar books in the "Read Also" column, or choose other free books by Ralph S Phillips to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
L) (tlif. T is, in D), This incidentally, proves that R(X, L) satisfies Eq. (13). Finally we note that the conditions of the theorem are satisfied by the functions y such that y(0) = and y, y', and y*' are absolutely continuous and all vanish outside a finite inter- val. Hence these functions lie in D; and since they are dense in 1^(0, oo) then by our definition L is a well-defined operator, Theorez: 2. 2 . The resolvent E(X, L) exists for all Im(X) > and is given in the Tisual way by (11).
It ...is clear that if the range of R(\, L) is contained in D then (2) will be satisfied. Let f e 1^(0, 00) and set y = R(X, L)f in Eq. (11). It is again clear that y, y* are absolutely continuous, that y and -y^' + q(x)y belong to 12(0, 00), and that y(0) = 0. Finally -9- V^ [y. H;(x, X^) ] = W^[v(x, \), v(x, \^) ] r ()(y. X) f(y) dy -'o + W^ |^()(x, X), v(x, \q) J [ vt/(y. X) f(y) dy.
z Now in the limit circle case toth f (J(yiX) f (y) dy — ^ limit and 7 v(yiX) f (y) dy —4 0. We now make use of two results due to Titchmarsh [5] (d 22 V namely, (16) .
What to read after Linear Ordinary Differential Operators of the Second Order?
You can find similar books in the "Read Also" column, or choose other free books by Ralph S Phillips to read onlineMoreLess
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