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Creators/Authors contains: "Larson, Simon"

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  1. ; (, Inventiones mathematicae)
    Abstract We consider the eigenvalues of the Dirichlet and Neumann Laplacians on a bounded domain with Lipschitz boundary and prove two-term asymptotics for their Riesz means of arbitrary positive order. Moreover, when the underlying domain is convex, we obtain universal, non-asymptotic bounds that correctly reproduce the two leading terms in the asymptotics and depend on the domain only through simple geometric characteristics. Important ingredients in our proof are non-asymptotic versions of various Tauberian theorems. 
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    Free, publicly-accessible full text available September 1, 2026
  2. ; ; (, Journal of Functional Analysis)
    Free, publicly-accessible full text available September 1, 2026
  3. ; ; (, Letters in Mathematical Physics)
    Abstract We prove a matrix inequality for convex functions of a Hermitian matrix on a bipartite space. As an application, we reprove and extend some theorems about eigenvalue asymptotics of Schrödinger operators with homogeneous potentials. The case of main interest is where the Weyl expression is infinite and a partially semiclassical limit occurs. 
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  4. ; (, Функциональный анализ и его приложения)
    Получена двучленная спектральная асимптотика для средних Риссасобственных значений оператора Лапласа на липшицевой области с граничными условиями Робена.Второе слагаемое в асимптотике оказывается тем же самым,что и в случае граничных условий Неймана. Такая асимптотика установленадля средних Рисса произвольного положительного порядка.Для порядков один и выше и при дополнительных предположениях о функции,входящей в граничные условия, также найден старший член асимптотикидля разности между средними Рисса собственных значений задач Робена и Неймана. 
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    Free, publicly-accessible full text available January 1, 2026
  5. ; (, Advances in Calculus of Variations)
    Abstract We consider Lane–Emden ground states with polytropic index 0 ≤ q - 1 ≤ 1 {0\leq q-1\leq 1} , that is, minimizers of the Dirichlet integral among L q {L^{q}} -normalized functions.Our main result is a sharp lower bound on the L 2 {L^{2}} -norm of the normal derivative in terms of the energy, which implies a corresponding isoperimetric inequality.Our bound holds for arbitrary bounded open Lipschitz sets Ω ⊂ ℝ d {\Omega\subset\mathbb{R}^{d}} , without assuming convexity. 
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  6. ; (, Probability and Mathematical Physics)
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  7. ; (, PARTIAL DIFFERENTIAL EQUATIONS, SPECTRAL THEORY, AND MATHEMATICAL PHYSICS)
    null (Ed.)
    DOI: 10.4171/ECR/18-1/9 
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    Accepted Manuscript Full Text Available
  8. ; ; ; ; ; ; ; (, The Journal of Geometric Analysis)
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