Functional Equations, Distributions and Approximate Identities
1990 ◽
Vol 42
(4)
◽
pp. 696-708
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Keyword(s):
The subject of this paper is the use of the theory of Schwartz distributions and approximate identities in studying the functional equationThe aj’s and b are complex-valued functions defined on a neighbourhood, U, of 0 in Rm, hj. U → Rn with hj(0) = 0 and fj, g: Rn → C for 1 ≦ j ≦ N. In most of what follows the aj's and hj's are assumed smooth and may be thought of as given. The fj‘s, b and g may be thought of as the unknowns. Typically we are concerned with locally integrable functions f1, … , fN such that, for each s in U, (1) holds for a.e. (almost every) x ∈ Rn, in the sense of Lebesgue measure.
1969 ◽
Vol 12
(6)
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pp. 837-846
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1964 ◽
Vol 16
◽
pp. 721-728
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1988 ◽
Vol 38
(3)
◽
pp. 351-356
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Keyword(s):
1985 ◽
Vol 97
(2)
◽
pp. 261-278
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1965 ◽
Vol 61
(4)
◽
pp. 889-894
◽
2017 ◽
Vol 60
(1)
◽
pp. 95-103
◽
1960 ◽
Vol 3
(2)
◽
pp. 113-120
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2016 ◽
Vol 94
(2)
◽
pp. 278-285
◽
Keyword(s):
2012 ◽
Vol 85
(2)
◽
pp. 202-216
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Keyword(s):
1970 ◽
Vol 11
(3)
◽
pp. 362-366
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Keyword(s):