In 1976, Drasin gave a complete solution to the inverse problem of Nevanlinna theory (value distribution theory),[2] which was posed by Rolf Nevanlinna in 1929.[3] In the 1930s, the problem was investigated by Nevanlinna and by, among others, Egon Ullrich(de) (1902–1957) with later investigations by Oswald Teichmüller (1913–1943), Hans Wittich, Le Van Thiem (1918–1991) and other mathematicians. Anatolii Goldberg (1930–2008) was the first to completely solve the inverse problem in the special case where the number of exceptional values is finite.[4] For entire functions the problem was solved in 1962 by Wolfgang Fuchs and Walter Hayman.[5] The general problem concerns the question of the existence of a meromorphic function at given values of the exceptional values and associated deficiency values and branching values (with constraints from the Nevanlinna theory). Drasin proved that there is a positive answer to Nevanlinna's problem.[6]
In 1994 Drasin was an Invited Speaker at the ICM in Zurich.[7] Since 1996 he is a co-editor of the Annals of the Finnish Academy of Sciences and a co-editor of Computational Methods in Function Theory. He was a co-editor of the American Mathematical Monthly from 1968 to 1971. From 2002 to 2004 he was a program director/analyst for the National Science Foundation.
with Clifford John Earle: On the boundedness of automorphic forms. Proc. Amer. Math. Soc. 19 (1968) 1039–1042. doi:10.1090/S0002-9939-1968-0239083-2
with Daniel F. Shea: Asymptotic properties of entire functions extremal for the theorem. Bull. Amer. Math. Soc. 75 (1969) 119–122. doi:10.1090/S0002-9904-1969-12169-5
with Daniel F. Shea: Pólya peaks and the oscillation of positive functions. Proc. Amer. Math. Soc. 34 (1972) 403–411. doi:10.1090/S0002-9939-1972-0294580-X
A meromorphic function with assigned Nevanlinna deficiencies. Bull. Amer. Math. Soc. 80 (1974) 766–768. doi:10.1090/S0002-9904-1974-13595-0
with Guang Hou Zhang, Lo Yang, and Allen Weitsman. Deficient values of entire functions and their derivatives. Proc. Amer. Math. Soc. 82 (1981) 607–612. doi:10.1090/S0002-9939-1981-0614887-9
with Eugene Seneta: A generalization of slowly varying functions . Proc. Amer. Math. Soc. 96 (1986) 470–472. doi:10.1090/S0002-9939-1986-0822442-5
"Proof of a conjecture of F. Nevanlinna concerning functions which have deficiency sum two." Acta Mathematica 158, no. 1 (1987): 1–94. doi:10.1007/BF02392256
with Pekka Pannka: "Sharpness of Rickman’s Picard theorem in all dimensions." Acta Mathematica 214, no. 2 (2015): 209–306. doi:10.1007/s11511-015-0125-x
^Drasin The inverse problem of the Nevanlinna theory , Acta Mathematica Vol. 138, 1976, pp. 83–151, doi:10.1007/BF02392314. Updated in: Drasin On Nevanlinna's Inverse Problem , Complex Variables, Theory and Application, Vol. 37, 1998, pp. 123–143 doi:10.1080/17476939808815127
^Nevanlinna Le théorème de Picard-Borel et la théorie des fonctions méromorphes, Gauthier-Villars 1929. Nevanlinna also solved a special case.
^Goldberg, Ostrovskii Value distribution of meromorphic functions, American Mathematical Society 2008, chapter 7.
^Nevanlinna himself was disappointed by the "inelegance" of the proof, according to Olli Lehto in Erhabene Welten – das Leben Rolf Nevanlinnas, Birkhäuser 2000, p. 80.
^Drasin, David. "Meromorphic functions: progress and problems." In Proceedings of the International Congress of Mathematicians, pp. 828–835. Birkhäuser Basel, 1995. doi:10.1007/978-3-0348-9078-6_12
External linksedit
David Drasin, Department of Mathematics, Purdue University
April 09, 2024
david, drasin, born, november, 1940, philadelphia, american, mathematician, specializing, function, theory, drasin, received, 1962, bachelor, degree, from, temple, university, 1966, doctorate, from, cornell, university, supervised, wolfgang, fuchs, clifford, j. David Drasin born 3 November 1940 Philadelphia is an American mathematician specializing in function theory Drasin received in 1962 his bachelor s degree from Temple University and in 1966 his doctorate from Cornell University supervised by Wolfgang Fuchs and Clifford John Earle Jr with thesis An integral Tauberian theorem and other topics 1 After that he was an assistant professor from 1969 an associate professor and from 1974 a full professor at Purdue University He was visiting professor in 2005 at the University of Kiel and in 2005 2006 at the University of Helsinki In 1976 Drasin gave a complete solution to the inverse problem of Nevanlinna theory value distribution theory 2 which was posed by Rolf Nevanlinna in 1929 3 In the 1930s the problem was investigated by Nevanlinna and by among others Egon Ullrich de 1902 1957 with later investigations by Oswald Teichmuller 1913 1943 Hans Wittich Le Van Thiem 1918 1991 and other mathematicians Anatolii Goldberg 1930 2008 was the first to completely solve the inverse problem in the special case where the number of exceptional values is finite 4 For entire functions the problem was solved in 1962 by Wolfgang Fuchs and Walter Hayman 5 The general problem concerns the question of the existence of a meromorphic function at given values of the exceptional values and associated deficiency values and branching values with constraints from the Nevanlinna theory Drasin proved that there is a positive answer to Nevanlinna s problem 6 In 1994 Drasin was an Invited Speaker at the ICM in Zurich 7 Since 1996 he is a co editor of the Annals of the Finnish Academy of Sciences and a co editor of Computational Methods in Function Theory He was a co editor of the American Mathematical Monthly from 1968 to 1971 From 2002 to 2004 he was a program director analyst for the National Science Foundation He is married and has three children Selected publications editTauberian theorems and slowly varying functions Trans Amer Math Soc 133 1968 333 356 doi 10 1090 S0002 9947 1968 0226017 4 with Clifford John Earle On the boundedness of automorphic forms Proc Amer Math Soc 19 1968 1039 1042 doi 10 1090 S0002 9939 1968 0239083 2 with Daniel F Shea Asymptotic properties of entire functions extremal for the cospr displaystyle cos pi rho nbsp theorem Bull Amer Math Soc 75 1969 119 122 doi 10 1090 S0002 9904 1969 12169 5 with Daniel F Shea Polya peaks and the oscillation of positive functions Proc Amer Math Soc 34 1972 403 411 doi 10 1090 S0002 9939 1972 0294580 X A meromorphic function with assigned Nevanlinna deficiencies Bull Amer Math Soc 80 1974 766 768 doi 10 1090 S0002 9904 1974 13595 0 with Guang Hou Zhang Lo Yang and Allen Weitsman Deficient values of entire functions and their derivatives Proc Amer Math Soc 82 1981 607 612 doi 10 1090 S0002 9939 1981 0614887 9 with Eugene Seneta A generalization of slowly varying functions Proc Amer Math Soc 96 1986 470 472 doi 10 1090 S0002 9939 1986 0822442 5 Proof of a conjecture of F Nevanlinna concerning functions which have deficiency sum two Acta Mathematica 158 no 1 1987 1 94 doi 10 1007 BF02392256 On a method of Holopainen and Rickman Israel Journal of Mathematics 101 no 1 1997 73 84 doi 10 1007 BF02760922 with Pekka Pannka Sharpness of Rickman s Picard theorem in all dimensions Acta Mathematica 214 no 2 2015 209 306 doi 10 1007 s11511 015 0125 xReferences edit David Drasin at the Mathematics Genealogy Project Drasin The inverse problem of the Nevanlinna theory Acta Mathematica Vol 138 1976 pp 83 151 doi 10 1007 BF02392314 Updated in Drasin On Nevanlinna s Inverse Problem Complex Variables Theory and Application Vol 37 1998 pp 123 143 doi 10 1080 17476939808815127 Nevanlinna Le theoreme de Picard Borel et la theorie des fonctions meromorphes Gauthier Villars 1929 Nevanlinna also solved a special case Goldberg Ostrovskii Value distribution of meromorphic functions American Mathematical Society 2008 chapter 7 Hayman s Meromorphic functions Clarendon Press 1964 chapter 4 Nevanlinna himself was disappointed by the inelegance of the proof according to Olli Lehto in Erhabene Welten das Leben Rolf Nevanlinnas Birkhauser 2000 p 80 Drasin David Meromorphic functions progress and problems In Proceedings of the International Congress of Mathematicians pp 828 835 Birkhauser Basel 1995 doi 10 1007 978 3 0348 9078 6 12External links editDavid Drasin Department of Mathematics Purdue University Retrieved from https en wikipedia org w index php title David Drasin amp oldid 1036626856, wikipedia, wiki, book, books, library,
