Anisotropic Shubin operators and eigenfunction expansions in Gelfand-Shilov spaces

We derive new results on the characterization of Gelfand-Shilov spaces Sνμ(Rn), μ, ν > 0, μ + ν ≥ 1 byGevrey estimates of the L2 norms of iterates of (m, k) anisotropic globally elliptic Shubin (or Γ) type operators, (- Δ)m/2 + |x>k with m, k ∈ 2ℕ being a model operator, and on the decay of the Fourier coefficients in the related eigenfunction expansions. Similar results are obtained for the spaces Σνμ(Rn), μ, ν > 0, μ + ν > 1, cf. (1.2). In contrast to the symmetric case μ = ν and k = m (classical Shubin operators) we encounter resonance type phenomena involving the ratio κ:= μ/ν; namely we obtain a characterization of Sνμ(Rn) and Σνμ(Rn) in the case μ = kt/(k + m), ν = mt/(k + m), t ≥ 1, that is, when κ = k/m ∈ ℚ. © 2019, The Hebrew University of Jerusalem.

Авторы
Cappiello M.1 , Gramchev T.2 , Pilipovic S.3 , Rodino L. 1, 4
Издательство
Springer New York LLC
Номер выпуска
2
Язык
Английский
Страницы
857-870
Статус
Опубликовано
Том
138
Год
2019
Организации
  • 1 Dipartimento di Matematica, Università di Torino, Via Carlo Alberto 10, Torino, 10123, Italy
  • 2 Dipartimento di Matematica e Informatica, Università di Cagliari, Via Ospedale 72, Cagliari, 09124, Italy
  • 3 Institute of Mathematics, University of Novi Sad, trg. D. Obradovica 4, Novi Sad, 21000, Serbia
  • 4 Rudn University, Miklukho-Maklay St. 6, Moscow, 117198, Russian Federation
Дата создания
24.12.2019
Дата изменения
24.12.2019
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/54999/