Weak spectral synthesis
HTML articles powered by AMS MathViewer
- by C. Robert Warner PDF
- Proc. Amer. Math. Soc. 99 (1987), 244-248 Request permission
Abstract:
As an approach to the union problem for sets of spectral synthesis ($S$-sets), the class of weak $S$-sets is introduced. This class contains all finite unions of $S$-sets, and it has many properties analogous to those of Calderón sets. It is closed under the operation of forming finite unions, but, in contrast to Calderón sets, it is not closed under countable unions.References
- John J. Benedetto, Spectral synthesis, Mathematische Leitfäden, B. G. Teubner, Stuttgart, 1975. MR 0622037
- Yngve Domar, On spectral synthesis in $\textbf {R}^{n}$, $n\geq 2$, Euclidean harmonic analysis (Proc. Sem., Univ. Maryland, College Park, Md., 1979) Lecture Notes in Math., vol. 779, Springer, Berlin, 1980, pp. 46–72. MR 576039
- Colin C. Graham and O. Carruth McGehee, Essays in commutative harmonic analysis, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 238, Springer-Verlag, New York-Berlin, 1979. MR 550606
- C. Herz, The ideal theorem in certain Banach algebras of functions satisfying smoothness conditions, Functional Analysis (Proc. Conf., Irvine, Calif., 1966) Academic Press, London; Thompson Book Co., Washington, D.C., 1967, pp. 222–234. MR 0226407
- Yitzhak Katznelson, An introduction to harmonic analysis, Second corrected edition, Dover Publications, Inc., New York, 1976. MR 0422992
- W. Kirsch and D. Müller, On the synthesis problem for orbits of Lie groups in $\textbf {R}^{n}$, Ark. Mat. 18 (1980), no. 2, 145–155. MR 608333, DOI 10.1007/BF02384687
- Detlef Müller, On the spectral synthesis problem for hypersurfaces of $\textbf {R}^{N}$, J. Functional Analysis 47 (1982), no. 2, 247–280. MR 664338, DOI 10.1016/0022-1236(82)90107-0
- Walter Rudin, Fourier analysis on groups, Interscience Tracts in Pure and Applied Mathematics, No. 12, Interscience Publishers (a division of John Wiley & Sons, Inc.), New York-London, 1962. MR 0152834
- Edgar Lee Stout, The theory of uniform algebras, Bogden & Quigley, Inc., Publishers, Tarrytown-on-Hudson, N.Y., 1971. MR 0423083
- N. Th. Varopoulos, Spectral synthesis on spheres, Proc. Cambridge Philos. Soc. 62 (1966), 379–387. MR 201908, DOI 10.1017/s0305004100039967 —, Algèbres tensorielles et analyse harmonique, Publ. Math. d’Orsay, Paris, 1967-1968.
- N. Th. Varopoulos, Tensor algebras and harmonic analysis, Acta Math. 119 (1967), 51–112. MR 240564, DOI 10.1007/BF02392079
- C. Robert Warner, A class of spectral sets, Proc. Amer. Math. Soc. 57 (1976), no. 1, 99–102. MR 410275, DOI 10.1090/S0002-9939-1976-0410275-7
Additional Information
- © Copyright 1987 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 99 (1987), 244-248
- MSC: Primary 43A45; Secondary 46J05
- DOI: https://doi.org/10.1090/S0002-9939-1987-0870779-7
- MathSciNet review: 870779