A result on nearness of functions and their regular -fraction expansions

Authors:
Lisa Jacobsen and Haakon Waadeland

Journal:
Proc. Amer. Math. Soc. **106** (1989), 741-750

MSC:
Primary 30B70; Secondary 40A15

DOI:
https://doi.org/10.1090/S0002-9939-1989-0967487-2

MathSciNet review:
967487

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We shall prove a "nearness"-result of the following type. If is a holomorphic function in and "sufficiently near" the function , then has a regular C-fraction expansion where .

**[1]**Rolf M. Hovstad,*Solution of a convergence problem in the theory of 𝑇-fractions*, Proc. Amer. Math. Soc.**48**(1975), 337–343. MR**0364612**, https://doi.org/10.1090/S0002-9939-1975-0364612-1**[2]**William B. Jones and Wolfgang J. Thron,*Continued fractions*, Encyclopedia of Mathematics and its Applications, vol. 11, Addison-Wesley Publishing Co., Reading, Mass., 1980. Analytic theory and applications; With a foreword by Felix E. Browder; With an introduction by Peter Henrici. MR**595864****[3]**O. Njàstad and H. Waadeland,*Strongly bounded holomorphic functions and PC-fractions*, submitted**[4]**W. J. Thron and Haakon Waadeland,*Analytic continuation of functions defined by means of continued fractions*, Math. Scand.**47**(1980), no. 1, 72–90. MR**600079**, https://doi.org/10.7146/math.scand.a-11875**[5]**Haakon Waadeland,*On 𝑇-fractions of functions holomorphic and bounded in a circular disc*, Norske Vid. Selsk. Skr. (Trondheim)**1964**(1964), no. 8, 19. MR**0177100****[6]**Haakon Waadeland,*General 𝑇-fractions corresponding to functions satisfying certain boundedness conditions*, J. Approx. Theory**26**(1979), no. 4, 317–328. MR**550679**, https://doi.org/10.1016/0021-9045(79)90068-6**[7]**Haakon Waadeland,*Limit-periodic general 𝑇-fractions and holomorphic functions*, J. Approx. Theory**27**(1979), no. 4, 329–345. MR**556783**, https://doi.org/10.1016/0021-9045(79)90122-9**[8]**-,*General**-expansions of bounded functions*, Mathematics no. 2 (1983), Univ. of Trondheim.**[9]**H. S. Wall,*Analytic Theory of Continued Fractions*, D. Van Nostrand Company, Inc., New York, N. Y., 1948. MR**0025596****[10]**L. Jacobsen, and H. Waadeland,*When does**have a regular**-fraction expansion or a normal Padé table*, to appear in Journ. of Comp. and Appl. Math.

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
30B70,
40A15

Retrieve articles in all journals with MSC: 30B70, 40A15

Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1989-0967487-2

Keywords:
Continued fractions,
-fractions,
regular -fractions,
-fraction expansions

Article copyright:
© Copyright 1989
American Mathematical Society