Infinite Determinants in the Theory of Mathieus And Hills Equations
Infinite Determinants in the Theory of Mathieus And Hills Equations
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In our eReader you can find the full English version of the book. Read Infinite Determinants in the Theory of Mathieus And Hills Equations 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 Infinite Determinants in the Theory of Mathieus And Hills Equations
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To quickly assess the difficulty of the text, read a short excerpt:
T2[. .. ]. In particular, if a ■ 0, b « 1, we find that (U) y2(x;o. , t) - / e^^"^ G(x, ^, t) d^), -X where G can be expanded in a power series in t which is everywhere convergent . As a function of the real variables ^ and x, G satisfies the partial differen- tial equation 2 2 (5) ^ - -^ + Stcos 2x G - 0.
dx 3^ 3G (6) G(x;ix, t) » X, QtJ^vi'it. X, t) -It sinx cosx .
The proof of Theorem U can be derived from Theorem X, p. 13 in the book by Paley and Wiener [^8 J . According to this theorem, th...e following two classes of functions are identical: (l) The class of all entire functions F(z) satisfying (7) |F(z)| - o(e^'^l) ; - 31 - (II) the class of all entire functions of the form +A (8) F(z) =/ f(u) e^^V, -A where f(u) belongs to Lp over (-A, A), It may suffice to prove (U), (5) and (6). Putting fn\ t \ sin 2cox (9) u^(x, co) - —^ and ) ^ (10) u^(x, co) - - ^ y sin 2a)(x-f) cos24 u^__j^(4) d?, o we find 00 (n) 72^*'"**^ " 21 ^^n^" » n«0 where the series on the right-hand side converges for all values of t.
What to read after Infinite Determinants in the Theory of Mathieus And Hills Equations?
You can find similar books in the "Read Also" column, or choose other free books by W Magnus to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
T2[. .. ]. In particular, if a ■ 0, b « 1, we find that (U) y2(x;o. , t) - / e^^"^ G(x, ^, t) d^), -X where G can be expanded in a power series in t which is everywhere convergent . As a function of the real variables ^ and x, G satisfies the partial differen- tial equation 2 2 (5) ^ - -^ + Stcos 2x G - 0.
dx 3^ 3G (6) G(x;ix, t) » X, QtJ^vi'it. X, t) -It sinx cosx .
The proof of Theorem U can be derived from Theorem X, p. 13 in the book by Paley and Wiener [^8 J . According to this theorem, th...e following two classes of functions are identical: (l) The class of all entire functions F(z) satisfying (7) |F(z)| - o(e^'^l) ; - 31 - (II) the class of all entire functions of the form +A (8) F(z) =/ f(u) e^^V, -A where f(u) belongs to Lp over (-A, A), It may suffice to prove (U), (5) and (6). Putting fn\ t \ sin 2cox (9) u^(x, co) - —^ and ) ^ (10) u^(x, co) - - ^ y sin 2a)(x-f) cos24 u^__j^(4) d?, o we find 00 (n) 72^*'"**^ " 21 ^^n^" » n«0 where the series on the right-hand side converges for all values of t.
What to read after Infinite Determinants in the Theory of Mathieus And Hills Equations?
You can find similar books in the "Read Also" column, or choose other free books by W Magnus to read onlineMoreLess
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