On convolution of entire probability densities
- 1 October 1998
- journal article
- research article
- Published by Taylor & Francis in Complex Variables and Elliptic Equations
- Vol. 36 (2) , 165-181
- https://doi.org/10.1080/17476939808815106
Abstract
Let t be a non-negative function of C 1[0, ∞) such that tt(0) = 0 and t′( r) ↑ ∞ as r ↑ ∞ We prove that there exists an entire function f non-negative on R and satisfying the following conditions: 1)0 < limsupr→∞ M(r, f) exp (−t(r)) < ∞, where 2)f ∈ L 1 (R); 3)sup{f(x): x ∈ R} = ∞; 4)ess sup{(f * f)( x) : x ∈ (α, β)} = ∞ for all non-empty intervals (α, β) ⊂ R.Keywords
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