Abstract:
Two methods for computing the integrals of rational functions over Rn are considered. The first is applicable to differentials with rational antiderivatives and uses the interpretation of Rn as a chain of integration in some toric compactification. The second method is based on the theory of multidimensional residues and the multidimensional version of the Sokhotskii formula for the jump of an integral.
Citation:
T. O. Ermolaeva, A. K. Tsikh, “Integration of rational functions over Rn by means of toric compactifications and multidimensional residues”, Sb. Math., 187:9 (1996), 1301–1318
\Bibitem{ErmTsi96}
\by T.~O.~Ermolaeva, A.~K.~Tsikh
\paper Integration of rational functions over $\mathbb R^n$ by means of toric compactifications and multidimensional residues
\jour Sb. Math.
\yr 1996
\vol 187
\issue 9
\pages 1301--1318
\mathnet{http://mi.mathnet.ru/eng/sm157}
\crossref{https://doi.org/10.1070/SM1996v187n09ABEH000157}
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Linking options:
https://www.mathnet.ru/eng/sm157
https://doi.org/10.1070/SM1996v187n09ABEH000157
https://www.mathnet.ru/eng/sm/v187/i9/p45
This publication is cited in the following 10 articles:
Irina A. Antipova, Timofey A. Efimov, Avgust K. Tsikh, “Mellin transforms for rational functions with quasi-elliptic denominators”, Zhurn. SFU. Ser. Matem. i fiz., 16:6 (2023), 738–750
T. Yu. Semenova, “Uslovie skhodimosti nesobstvennykh kratnykh integralov v terminakh mnogogrannikov Nyutona”, Chebyshevskii sb., 22:1 (2021), 328–339
Rubin D., “Asymptotic Slopes of the Aubin-Yau Functional and Calculation of the Donaldson-Futaki Invariant”, J. Geom. Anal., 28:3 (2018), 2812–2833
E. V. Zubchenkova, “Ob integralnom priznake skhodimosti dlya mnogomernykh ryadov Dirikhle”, Sib. elektron. matem. izv., 11 (2014), 76–86
Lisa Nilsson, Mikael Passare, “Mellin Transforms of Multivariate Rational Functions”, J Geom Anal, 2011
Elena V. Zubchenkova, “Integralnyi priznak skhodimosti nekotorykh kratnykh ryadov”, Zhurn. SFU. Ser. Matem. i fiz., 4:3 (2011), 344–349
Olga S. Ulvert, “Ob integralakh po dvumernym kompaktnym kompleksnym toricheskim mnogoobraziyam”, Zhurn. SFU. Ser. Matem. i fiz., 3:4 (2010), 544–555
Oksana V. Znamenskaya, Aleksei V. Schuplev, “O veschestvennykh toricheskikh mnogoobraziyakh razmernosti dva”, Zhurn. SFU. Ser. Matem. i fiz., 2:4 (2009), 401–409
Proc. Steklov Inst. Math., 253 (2006), 256–274
A. V. Putilina, “Asymptotics of the volume function for the set of lesser values of a polynomial in Rn”, Russian Math. (Iz. VUZ), 44:6 (2000), 14–21
Citation in format AMSBIB
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