Completeness of $\{\textrm {sin}\ nx+Ki$ $\textrm {cos}\ nx\}$
HTML articles powered by AMS MathViewer
- by Jonathan I. Ginsberg PDF
- Proc. Amer. Math. Soc. 29 (1971), 291-293 Request permission
Abstract:
Let ${\mathbf {C}}[ {a,b} ]$ be the space of continuous functions on the interval $[ {a,b} ]$. It is shown that the set of functions $\{ {\sin nx + Ki\cos nx} \}_{n = 1}^\infty ,K \ne \pm 1$, is incomplete in ${\mathbf {C}}[ {0,\pi + a} ],a > 0$.References
- Robert Feinerman and D. J. Newman, Completeness of $\{A$ $\textrm {sin}\ nx+$ $b$ $\textrm {cos}\ nx\}$ on $[o,\,\pi ]$, Michigan Math. J. 15 (1968), 305β312. MR 235380
- Norman Levinson, Gap and Density Theorems, American Mathematical Society Colloquium Publications, Vol. 26, American Mathematical Society, New York, 1940. MR 0003208, DOI 10.1090/coll/026
- Antoni Zygmund, Trigonometrical series, Chelsea Publishing Co., New York, 1952. 2nd ed. MR 0076084
Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 29 (1971), 291-293
- MSC: Primary 42.17
- DOI: https://doi.org/10.1090/S0002-9939-1971-0276679-6
- MathSciNet review: 0276679