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Original Articles

The Cauchy integral formula and distributional integration

Pages 1854-1868 | Received 03 Sep 2018, Accepted 30 Nov 2018, Published online: 20 Dec 2018

References

  • Conway JB. Functions of one complex variable. New York: Springer Verlag; 1978.
  • Fatou P. Séries trigonométriques et séries de Taylor. Acta Math. 1906;30:335–400. doi: 10.1007/BF02418579
  • Duren PL. Theory of Hp spaces. New York: Dover; 2000. (reprint of the Academic Press 1970 edition).
  • Estrada R, Vindas J. A general integral. Disertationes Mathematicae (Rozprawy Mat). 2012;483. 49 pages.
  • Estrada R, Kanwal RP. Distributional boundary values of harmonic and analytic functions. J Math Anal Appl. 1982;89:262–289. doi: 10.1016/0022-247X(82)90102-0
  • Natanson IP. Theory of functions of a real variable. Vol. 2. New York: Frederick Ungar Publishing; 1960.
  • Gordon RA. The integrals of Lebesgue, Denjoy, Perron, and Henstock. Providence: Amer. Math. Soc; 1994.
  • Romanovski P. Essai d'une exposition de l'integrale de Denjoy sans nombres transfini. Fund Math. 1932;19:38–44. doi: 10.4064/fm-19-1-38-44
  • Kanwal RP. Generalized functions: theory and technique. 3rd ed. Boston (MA): Birkhäuser; 2004.
  • Schwartz L. Théorie des distributions. Paris: Hermann; 1966.
  • Campos Ferreira J. Introduction to the theory of distributions. London: Longman; 1997.
  • Estrada R, Kanwal RP. A distributional approach to asymptotics. Theory and applications. 2nd ed. Boston (MA): Birkhäuser; 2002.
  • Pilipović S, Stanković B, Takači A. Asymptotic behavior and stieltjes transformation of distributions. Leipzig: Teubner-Texte zur Mathmatik; 1990.
  • Pilipović S, Stanković B, Vindas J. Asymptotic behavior of generalized functions. Singapore: World Scientific; 2011.
  • Vladimirov VS, Drozhzhinov YN, Zavialov BI. Tauberian theorems for generalized functions. Dordrecht: Kluwer Academic Publishers Group; 1988.
  • Estrada R. Some series of distributionally integrable functions. Transyl. J. Math. Mech. preprint, 2018 (submitted).
  • Łojasiewicz S. Sur la valeur et la limite d'une distribution en un point. Studia Math. 1957;16:1–36. doi: 10.4064/sm-16-1-1-36
  • Estrada R. Distributions that are functions. Linear and non-linear theory of generalized functions and its applications, pp. 91–110, Banach Center Publ. 88, Polish Acad. Sci. Inst. Math., Warsaw; 2010.
  • Mikusińksi P. and Ostaszewski, K: Embedding Henstock integrable functions into the space of Schwartz distributions. Real Anal Exchange. 1988-89;14:24–29.
  • Antosik P, Mikusiński J, Sikorski R. Theory of distributions. The sequential approach. Warsaw: Elsevier Scientific Publishing Co., PWN–Polish Scientific Publishers; 1973.
  • Sebastião e Silva J. Integrals and orders of growth of distributions. Theory of Distributions. (Proc. Internat. Summer Inst., Lisbon, 1964), pp. 327–390, Inst. Gulbenkian Ci., Lisbon; 1964.
  • Sikorski R. Integrals of distributions. Studia Math. 1961;20:119–139. doi: 10.4064/sm-20-2-119-139
  • Talvila E. The distributional Denjoy integral. Real Anal Exchange. 2008;33:51–82. doi: 10.14321/realanalexch.33.1.0051
  • Estrada R. Boundary values of analytic functions without distributional point values. Tamkang J Math. 2004;35:53–60.
  • Estrada R. One-sided cluster sets of distributional boundary values of analytic functions. Complex Var Elliptic Equ. 2006;51:661–673. doi: 10.1080/17476930600709171
  • Pommerenke C. Boundary behaviour of conformal maps. Berlin: Springer Verlag; 1992.
  • Collingwood EF, Lohwater AJ. The theory of cluster sets. Cambridge: Cambridge University Press; 1966.
  • Zielézny Z. Über die Mengen der regulären und singulären Punkte einer Distribution. Studia Math. 1960;19:27–52. doi: 10.4064/sm-19-1-27-52
  • Zygmund A. Trigonometric series. Cambridge: Cambridge Mathematical Library; 2002.
  • Vindas J, Estrada R. A tauberian theorem for distributional point values. Arch Math (Basel). 2008;91:247–253. doi: 10.1007/s00013-008-2683-z
  • Menne U. Pointwise differentiability of higher order for distributions, preprint.
  • Vindas J, Estrada R. On the point behavior of Fourier series and conjugate series. Z Anal Anwend. 2010;29:487–504.

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