Boundary Values of Potential Functions Prescribed Along Interior Paths
Boundary Values of Potential Functions Prescribed Along Interior Paths
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In our eReader you can find the full English version of the book. Read Boundary Values of Potential Functions Prescribed Along Interior Paths 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 Boundary Values of Potential Functions Prescribed Along Interior Paths
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1). The integral in (3. 1) can be written i---a^ f tj>(cQ da 27r ^ [a-re^^Ha-re 1 ^] i9 or, if we replace e by z, as o o 2tt r -a P ft (a) da 2Tr - [«. R«- ao «][a. J2S] This integral defines a function of the complex variable z = pe i6, analytic in the domain a/r < |z| < r/a. It shows that (3. 1) possesses a solution only if the prescribed function f(9) is an analytic periodic function of 9 which allows continua- tion into the annular domain defined above. If this condition is satisfied, the equation (3. 1) can presumably be solved by using any - ■ : 17 using any one of the methods of Section 2. [In order to solve (5. 1) by the transform method III, this method must of course be changed to a finite transform method. ] Let us choose method II v;hich depends on the existence of a semi-group property of the transform because of the four methods this one seems the most challenging, and most likely to involve a nev; Idea. If we put A : a/r < 1 vie can virite (J-. L) In the form (j)(q) da (3.
What to read after Boundary Values of Potential Functions Prescribed Along Interior Paths?
You can find similar books in the "Read Also" column, or choose other free books by Arthur S Peters to read online
To quickly assess the difficulty of the text, read a short excerpt:
1). The integral in (3. 1) can be written i---a^ f tj>(cQ da 27r ^ [a-re^^Ha-re 1 ^] i9 or, if we replace e by z, as o o 2tt r -a P ft (a) da 2Tr - [«. R«- ao «][a. J2S] This integral defines a function of the complex variable z = pe i6, analytic in the domain a/r < |z| < r/a. It shows that (3. 1) possesses a solution only if the prescribed function f(9) is an analytic periodic function of 9 which allows continua- tion into the annular domain defined above. If this condition is satisfied, the equation (3. 1) can presumably be solved by using any - ■ : 17 using any one of the methods of Section 2. [In order to solve (5. 1) by the transform method III, this method must of course be changed to a finite transform method. ] Let us choose method II v;hich depends on the existence of a semi-group property of the transform because of the four methods this one seems the most challenging, and most likely to involve a nev; Idea. If we put A : a/r < 1 vie can virite (J-. L) In the form (j)(q) da (3.
What to read after Boundary Values of Potential Functions Prescribed Along Interior Paths?
You can find similar books in the "Read Also" column, or choose other free books by Arthur S Peters to read online
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