On approximation of functions by p–Faber-Laurent rational functions

References

• Çavuş A, Israfilov DM. Approximation by Faber-Laurent rational functions in the mean of functions of the class Lp (Γ) with 1 1 < p < ∞. Approx. Theory Appl. 1995;11:105–118.
   Google Scholar
• Israfilov DM. Approximation by p–Faber polynomials in the weighted Smirnov class Ep (G, ω) and the Bieberbach polynomials. Constr. Approx. 2001;17:335–351.
   Web of Science ®Google Scholar
• Israfilov DM. Approximation by p–Faber-Laurent rational functions in the weighted Lebesgue spaces. Czechoslovak Math. J. 2004;54:751–765.
   Web of Science ®Google Scholar
• Suetin PK. Series of Faber polynomials. Vol. 1. Reading (MA): Gordob and Breack; 1998.
   Google Scholar
• Gaier D. Lectures on complex approximation. Boston-Stuttgart: Birkhäuser-Verlag; 1987.
   Google Scholar
• Markushevich AI. Theory of analytic functions. Vol. 2. Moscow: Izdatelstvo Nauka; 1968.
   Google Scholar
• Kocharyan GS. On a generalization of the Laurent and Fourier series. Izv. Akad. Nauk Arm. SSR Ser. Fiz.-Mat. Nauk. 1958;11:3–14. Russian.
   Google Scholar
• Duren PL. Theory of H^p spaces. New York (NY): Academic Press; 1970.
   Google Scholar
• Golusin GM. Geometric theory of functions of a complex variable. Vol. 26, Translation of mathematical monographs. Providence (RI): AMS; 1968.
   Google Scholar
• David G. Operateurs integraux singulers sur certaines courbes du plan complexe [Singular integral operators on some curves in complex plane]. Ann. Sci. Ecol. Norm. Super. 1984;4:157–189.
   Google Scholar
• Havin VP. Continuity in Lp of an integral operator with the Cauchy kernel (Russian, English Summary). Vestnik Leningrad Univ. 1967;22:103 MR 36 #, 1623.
   Google Scholar
• Walsh JL, Russel HG. Integrated continuity conditions and degree of approximation by polynomials or by bounded analytic functions. Trans. Amer. Math. Soc. 1959;92:355–370.
   Google Scholar
• Alper SY. Approximation in the mean of analytic functions of class Ep. In: Investigations on the modern problems of the function of a complex variable. Gos. Izdat. Fiz.-Mat. Lit.; Moscow; 1960. p. 272–286. Russian.
   Google Scholar
• Andersson JE. On the degree of polynomial approximation in Ep(D). J. Approx. Theory. 1977;19:61–68.
   Web of Science ®Google Scholar
• Ibragimov II, Mamedkhanov DI. A constructive characterization of a certain class of functions. Dokl. Akad. Nauk SSSR. 223;1975:35–37; Soviet Math. Dokl. 1976;4:820–823.
   Google Scholar
• Israfilov DM. Approximation in weighted Smirnov classes. East J. Approx. 2005;11:91–102.
   Google Scholar
• Israfilov DM. Approximate properties of the generalized Faber series in an integral metric. Izv. Akad. Nauk Azerb. SSR Ser. Fiz.-Tekh. Math. Nauk. 1987;2:10–14. Russian.
   Google Scholar
• Kokilashvili VM. A direct theorem on mean approximation of analytic functions by polynomials. Soviet Math. Dokl. 1969;10:411–414.
   Google Scholar
• Mamedkhanov DI. Approximation in complex plane and singular operators with a Cauchy kernel [dissertation Doct. Phys-math.nauk.]. Tbilisi: The University of Tbilisi; 1984. Russian.
   Google Scholar
• Andrievskii VV. Approximation of functions by partial sums in Faber polynomials on continua with a nonzero local geometric characteristic. Ukrain. Mat. Zh. 1980;32:3–10. Russian.
   Google Scholar
• Kocharyan GS. Approximation by rational functions in a complex domain. Izv. Akad. Nauk Arm SSR Ser. Fiz.-Mat. Nauk. 1958;11:53–77. Russian.
   Google Scholar
• Tietz H. Laurent-Trennung und zweifach unendliche Faber Systeme [Separation and doubly infinite Faber systems]. Math. Ann. 1955;129:431–450.
   Web of Science ®Google Scholar
• Tietz H. Faber series and the Laurent decomposition. Michigan Math. J. 1957;4:157–179.
   Google Scholar
• Ji-feng Xie, Ming Zhang. A complex approximation on doubly-connected domain. J. Fudan Univ. Nat. Sci. 2005;44:328–331.
   Google Scholar
• Jafarov SZ. Approximation by polynomials and rational functions in Orlicz spaces. J. Comput. Anal. Appl. (JoCAAA). 2011;13:953–962.
   Web of Science ®Google Scholar
• Andrievskii VV, Israfilov DM. Approximations of functions on quasiconformal curves by rational functions. Izv. Akad. Nauk Azerb. SSR Ser. Fiz-Tekhn. Math. Nauk. 1980;36:21–26. Russian.
   Google Scholar
• Akgün R, Israfilov DM. Approximation and moduli of fractional orders in Smirnov-Orlicz classes. Glas. Mat. Ser. III. 2008;43:121–136.
   Web of Science ®Google Scholar
• Guven A, Israfilov DM. Approximation in rearrangement invariant spaces in Carleson curves. East J. Approx. 2006;12:381–395.
   Google Scholar
• Guven A, Israfilov DM. Rational approximation in Orlicz spaces on Carleson curves. Bull. Belg. Math. Soc. Simon Stevin. 2005;12:223–234.
   Web of Science ®Google Scholar
• Israfilov DM, Oktay B, Akgün R. Approximation in Smirnov-Orlicz classes. Glas. Mat. Ser. III. 2005;40:87–102.
   Google Scholar
• Israfilov DM, Akgün R. Approximation by polynomials and rational functions in weighted Rearrangement invariant spaces. J. Math. Anal. Appl. 2008;346:489–500.
   Web of Science ®Google Scholar
• Jafarov SZ. A direct and an inverse theorem in the theory of approximation on quasiconformal curves. Izv. Akad. Nauk Azerb. SSR Ser. Fiz-Tekhn. Mat. Nauk. 1987;8:8–11. Russian.
   Google Scholar
• Jafarov SZ. Approximation of functions by Faber-Laurent rational functions on closed quasiconformal curves. Trans. Natl. Acad. Sci. Azerb. Ser. Phys.-Tech. Math. Sci. 2008;28:97–102.
   Google Scholar
• Jafarov SZ. Approximation of functions by rational functions on closed curves of the complex plane. Arab. J. Sci. Eng. 2011;36:1529–1534.
   Web of Science ®Google Scholar
• Jafarov SZ. Approximation by rational functions in Smirnov-Orlicz classes. J. Math. Anal. Appl. 2011;379:870–877.
   Web of Science ®Google Scholar
• Jafarov SZ. On approximation in weighted Smirnov-Orlicz classes. Complex Var. Elliptic Equ. 2012;57:567–572.
   Web of Science ®Google Scholar
• Ramazanov A-RK. On approximation by polynomials and rational functions in Orlicz spaces. Anal. Math. 1984;10:117–132.
   Google Scholar
• Walsh JL. On approximation to analytic functions by rational functions of best approximation. Math. Z. 1934;38:163–176.
   Google Scholar
• Walsh JL. Interpolation and approximation by rational functions in the complex domain. Amer. Math. Soc. Colloq. Publ. Vol. 20. Providence (RI): Amer. Math. Soc.; 1935. Russian transl. Moscow (IL); 1961.
   Google Scholar