It is well-known that, by applying standard inequalities to functions with values in an appropriate Banach space, the applicability of these inequalities can often be usefully extended. For this reason, it is noteworthy that, whereas M. Riesz' original proof of his well-known inequality for the
β¦ LIBER β¦
On limiting values of an integral of Cauchy type for functions of zygmund classes
β Scribed by V. K. Dzyadyk; I. A. Shevchuk
- Book ID
- 112479618
- Publisher
- Springer
- Year
- 1972
- Tongue
- English
- Weight
- 878 KB
- Volume
- 24
- Category
- Article
- ISSN
- 0041-5995
No coin nor oath required. For personal study only.
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The problem of the numerical evaluation of Cauchy principal value integrals of oscillatory functions 1 -1 e iΟx f (x) x-Ο dx, where -1 < Ο < 1, has been discussed. Based on analytic continuation, if f is analytic in a sufficiently large complex region G containing [-1, 1], the integrals can be tran