I have been stuck in the following problem, who can help me out?
Problem： Given that f(x,y) is a continuous function defined on unit circle \(\displaystyle S^1\, : \, x^2\, +\, y^2\, =\,1,\) prove that:
. . . . .\(\displaystyle \displaystyle{ \lim_{t\, \to \, 1^{-} } }\,\) \(\displaystyle \dfrac{\sqrt{1\, -\, t^2\,}}{2\pi} \) \(\displaystyle \displaystyle{ \int_{S^1} }\,\) \(\displaystyle \dfrac{f(x,\, y)}{1\, -\, tx}\, ds\, =\, f(1,\, 0) \)
Problem： Given that f(x,y) is a continuous function defined on unit circle \(\displaystyle S^1\, : \, x^2\, +\, y^2\, =\,1,\) prove that:
. . . . .\(\displaystyle \displaystyle{ \lim_{t\, \to \, 1^{-} } }\,\) \(\displaystyle \dfrac{\sqrt{1\, -\, t^2\,}}{2\pi} \) \(\displaystyle \displaystyle{ \int_{S^1} }\,\) \(\displaystyle \dfrac{f(x,\, y)}{1\, -\, tx}\, ds\, =\, f(1,\, 0) \)
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