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Keywords:
temperate distribution; multiplication operator; inductive limit of locally convex spaces; projective limit of locally convex spaces; generalized derivative; Sobolev derivative
temperate distribution; multiplication operator; inductive limit of locally convex spaces; projective limit of locally convex spaces; generalized derivative; Sobolev derivative
Summary:
Spaces $\mathcal{O}_q$, $q \in \mathbb{N}$, of multipliers of temperate distributions introduced in an earlier paper of the first author are expressed as inductive limits of Hilbert spaces.
References:
[1] Schwartz, L.: Théorie des Distributions. Hermann, Paris, 1966. MR 0209834 | Zbl 0149.09501
[2] Horváth, J.: Topological Vector Spaces and Distributions, Vol. 1. Addison-Wisley, Reading, 1966.
[3] Kučera, J.: Fourier $L_2$-transform of distributions. Czechoslovak Math. J. 19 (1969), 143–153. MR 0240616
[4] Kučera, J.: On multipliers of temperate distributions. Czechoslovak Math. J. 21 (1971), 610–618. MR 0293391
[5] Kučera, J., McKennon, K.: Certain topologies on the space of temperate distributions and its multipliers. Indiana Univ. Math. 24 (1975), 773–775. DOI 10.1512/iumj.1975.24.24061 | MR 0358344
[6] Kučera, J.: Extension of the L. Schwartz space $\mathcal{O}_M$ of multipliers of temperate distributions. J. Math. Anal. Appl. 56 (1976), 368–372. DOI 10.1016/0022-247X(76)90049-4 | MR 0417778
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