Extension of Privaloff’s theorem to ultraspherical expansions
HTML articles powered by AMS MathViewer
- by Allan J. Fryant PDF
- Proc. Amer. Math. Soc. 71 (1978), 49-53 Request permission
Abstract:
Privaloff’s theorem which relates the boundary continuity of $\operatorname {Re} (f)$ to that of f, f analytic on a disk, is extended to ultraspherical expansions.References
- N. K. Bary, A treatise on trigonometric series. Vols. I, II, A Pergamon Press Book, The Macmillan Company, New York, 1964. Authorized translation by Margaret F. Mullins. MR 0171116 R. Courant and D. Hilbert, Methods of mathematical physics, Vol. 2, Interscience, New York, 1962.
- Arthur Erdélyi, Singularities of generalized axially symmetric potentials, Comm. Pure Appl. Math. 9 (1956), 403–414. MR 84050, DOI 10.1002/cpa.3160090312
- Robert P. Gilbert, Function theoretic methods in partial differential equations, Mathematics in Science and Engineering, Vol. 54, Academic Press, New York-London, 1969. MR 0241789
- Robert P. Gilbert, On the singularities of generalized axially symmetric potentials, Arch. Rational Mech. Anal. 6 (1960), 171–176 (1960). MR 120478, DOI 10.1007/BF00276160
- G. M. Goluzin, Geometric theory of functions of a complex variable, Translations of Mathematical Monographs, Vol. 26, American Mathematical Society, Providence, R.I., 1969. MR 0247039, DOI 10.1090/mmono/026
- G. H. Hardy and J. E. Littlewood, Some properties of fractional integrals. II, Math. Z. 34 (1932), no. 1, 403–439. MR 1545260, DOI 10.1007/BF01180596
- J. Priwaloff, Sur les fonctions conjuguées, Bull. Soc. Math. France 44 (1916), 100–103 (French). MR 1504751, DOI 10.24033/bsmf.965
- G. Szegö, On the singularities of zonal harmonic expansions, J. Rational Mech. Anal. 3 (1954), 561–564. MR 62880, DOI 10.1512/iumj.1954.3.53028
- Francesco G. Tricomi, Vorlesungen über Orthogonalreihen, Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete, Band LXXVI, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1955 (German). MR 0070746, DOI 10.1007/978-3-662-13399-6
- Alexander Weinstein, Generalized axially symmetric potential theory, Bull. Amer. Math. Soc. 59 (1953), 20–38. MR 53289, DOI 10.1090/S0002-9904-1953-09651-3
Additional Information
- © Copyright 1978 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 71 (1978), 49-53
- MSC: Primary 42A56; Secondary 33A45
- DOI: https://doi.org/10.1090/S0002-9939-1978-0481900-1
- MathSciNet review: 0481900