Computational Methods and Function Theory 3 (2003), No. 1, 359--383
Copyright Heldermann Verlag 2003
Norair Arakelian
arakelian@instmath.sci.am, Institute of Mathematics of the National Academy of Sciences of Armenia, Marshal Bagramian ave. 24B, Yerevan 375019, Armenia.
Henrik Shahgholian
henriksh@math.kth.se, Department of Mathematics of the Royal Institute of Technology, 100 44 Stockholm, Sweden.
For a functions f, continuous on a closed strip S and holomorphic on its interior, we discuss the problem of uniform and tangential approximation on S by entire functions with simultaneous estimation of their growth. For the optimization of this growth (depending on the growth of f on S and on the differential properties of f on partial-S) we develop an adequate approximation technique. In this way we obtain sharp new results on uniform and tangential approximation by entire functions of finite order. These sharpen results of H. Kober [Trans. Amer. Math. Soc. 54 (1943) 70--82; Trans. Amer. Math. Soc. 54 (1944) 7--31] and M. V. Keldysh [Dokl. Akad. Nauk SSSR 47 (1945), No. 4, 239--241 (in Russian)], and other authors.
Keywords: Uniform approximation, tangential approximation, entire function.
MSC 2000: Primary 30E10; Secondary 30Dxx.
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