Anisotropic Shubin operators and eigenfunction expansions in Gelfand-Shilov spaces
| Autor: | Stevan Pilipović, Marco Cappiello, Todor Gramchev, Luigi Rodino |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Functional analysis
General Mathematics 010102 general mathematics Resonance Characterization (mathematics) Type (model theory) Eigenfunction anisotropic Shubin-type operators Gelfand-Shilov spaces eigenfunction expansions 01 natural sciences 010101 applied mathematics Combinatorics Operator (computer programming) Iterated function anisotropic Shubin-type operators 0101 mathematics Gelfand-Shilov spaces Fourier series Analysis eigenfunction expansions Mathematics |
| Zdroj: | Journal d'Analyse Mathematique. 138(2):857-870 |
| ISSN: | 0021-7670 |
| Popis: | We derive new results on the characterization of Gelfand-Shilov spaces $$\mathcal{S}_{\nu}^{\mu}(\mathbb{R}^n)$$ , 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 $$\Sigma_{\nu}^{\mu}(\mathbb{R}^n)$$ , 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 $$\mathcal{S}_{\nu}^{\mu}(\mathbb{R}^n)$$ and $$\Sigma_{\nu}^{\mu}(\mathbb{R}^n)$$ in the case μ = kt/(k + m), ν = mt/(k + m), t ≥ 1, that is, when κ = k/m ∈ ℚ. |
| Databáze: | OpenAIRE |
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