Exponential bound of the integral of Hermite functions product with Gaussian weight

In this paper we derive a bound on the integral of a product of two Hermite-Gaussian functions with a Gaussian weight. We prove that such integrals decay exponentially in the difference of the indices of the Hermite-Gaussian functions. Such integrals arise naturally in mathematical physics and applied mathematics. The estimate is applied to a variational problem related to a Strichartz functional. (c) 2022 Elsevier Inc. All rights reserved.

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In this paper, a bound on the integral of a product of two Hermite-Gaussian functions with a Gaussian weight is derived. It is proven that such integrals decay exponentially as the difference of the indices of the Hermite-Gaussian functions. These integrals naturally arise in mathematical physics and applied mathematics. The estimate is applied to a variational problem related to a Strichartz functional.