J. Vaaler

activity

20052023

most citedGaussian Subordination for the Beurling-Selberg Extremal Problem

42 citations · 105 across the 14 of their papers we have counts for

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4 papers · 1 filter

math.CA2010★ 42 cited

Gaussian Subordination for the Beurling-Selberg Extremal Problem

Emanuel Carneiro, Friedrich Littmann, Jeffrey D. Vaaler

We determine extremal entire functions for the problem of majorizing, minorizing, and approximating the Gaussian function $e^{- π λ x^{2}}$ by entire functions of exponential type. This…

math.CA2008★ 17 cited

Some extremal functions in Fourier analysis, III

Emanuel Carneiro, Jeffrey D. Vaaler

We obtain the best approximation in $L^{1} (R)$ , by entire functions of exponential type, for a class of even functions that includes $e^{- λ ∣ x ∣}$ , where $λ > 0$ , $lo g ∣ x ∣$ and $∣ x ∣^{α}$ …

math.CA2008★ 37 cited

Some extremal functions in Fourier analysis, II

Emanuel Carneiro, Jeffrey D. Vaaler

We obtain extremal majorants and minorants of exponential type for a class of even functions on $R$ which includes $lo g ∣ x ∣$ and $∣ x ∣^{α}$ , where $- 1 < α < 1$ . We also give periodic…

math.CA2005

Generalizations of Goncalves' inequality

Peter Borwein, Michael J. Mossinghoff, Jeffrey D. Vaaler

If $F$ is a polynomial with complex coefficients, leading term $a_{N}$ , and roots $α_{1}$ , ..., $α_{N}$ , then Gonçalves' inequality states that $∥ F ∥_{2}^{2}$ is bounded below by $\abs{a_N}…