Some Integral Equations Related to Abels Equation And the Hilbert Transform
Some Integral Equations Related to Abels Equation And the Hilbert Transform
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9) and (4. 10) yield r. Tin """iv -ttIv [k-ljlke -e ]H^) (4. 11) sin TTV d IT dz TTiv r f(adc ^ vo-^iv r f(c)dc / (z-C) TTV + ke (z-C) 1^ az za which gives the solution of (4. 3).
We can now show the solution of (4. 12) ^aC (j)(z)dz _ r (t)(z)dz (^z)^ ' J (z-C)'' f(C) which is a generalization of the basic equation (4. 15) ^ (l)(z)d; z-C - f(a If in equation (4. 3) we take (C-z) = e (z-O -TTiv When z is on C»^, and take k = -e", then (4. 3) reduces to (3 CI (4. 12); and (4. 11) shows that 21 (4.... 14) ())(z, v) = i^-¥ f(C)d^ d dz (z-C)'-^ c ^ za f(C)dC (^z)l-^ is the solution of (4. 12). As a check it can be verified that If we Integrate (4. L4) and then take the limit of the resulting equation as v Is allowed to approach 1, the limit process gives lim (|)(z, v) ^ \ (£ ^ C)dC which is the well known solution of 4)(z)dz (})(z)dz f(C) or ^ il^ . - f(0 5. An Integral Equation with the Kernel sgn(C-x)/| sin Tr(C-x) | There are some interesting Integral equations of the form J^k(e, x) ^(x) dx = gin which can be solved by transforming them into (4.
What to read after Some Integral Equations Related to Abels Equation And the Hilbert Transform?
You can find similar books in the "Read Also" column, or choose other free books by Arthur S Peters to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
9) and (4. 10) yield r. Tin """iv -ttIv [k-ljlke -e ]H^) (4. 11) sin TTV d IT dz TTiv r f(adc ^ vo-^iv r f(c)dc / (z-C) TTV + ke (z-C) 1^ az za which gives the solution of (4. 3).
We can now show the solution of (4. 12) ^aC (j)(z)dz _ r (t)(z)dz (^z)^ ' J (z-C)'' f(C) which is a generalization of the basic equation (4. 15) ^ (l)(z)d; z-C - f(a If in equation (4. 3) we take (C-z) = e (z-O -TTiv When z is on C»^, and take k = -e", then (4. 3) reduces to (3 CI (4. 12); and (4. 11) shows that 21 (4.... 14) ())(z, v) = i^-¥ f(C)d^ d dz (z-C)'-^ c ^ za f(C)dC (^z)l-^ is the solution of (4. 12). As a check it can be verified that If we Integrate (4. L4) and then take the limit of the resulting equation as v Is allowed to approach 1, the limit process gives lim (|)(z, v) ^ \ (£ ^ C)dC which is the well known solution of 4)(z)dz (})(z)dz f(C) or ^ il^ . - f(0 5. An Integral Equation with the Kernel sgn(C-x)/| sin Tr(C-x) | There are some interesting Integral equations of the form J^k(e, x) ^(x) dx = gin which can be solved by transforming them into (4.
What to read after Some Integral Equations Related to Abels Equation And the Hilbert Transform?
You can find similar books in the "Read Also" column, or choose other free books by Arthur S Peters to read onlineMoreLess
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