Related papers: Anisotropic Shubin operators and eigenfunctions ex…
We obtain a characterization of ${\mathcal S}^{\{M_p\}}_{\{M_p\}}(\mathbb R^n)$ and $\mathcal {S}^{(M_p)}_{(M_p)}(\mathbb {R}^n)$, the general Gelfand-Shilov spaces of ultradifferentiable functions of Roumieu and Beurling type, in terms of…
We consider the anisotropic Shubin operators $(-\Delta)^m + \vert x\vert^{2k}$ acting on the space $L^2(\mathbb R^n)$, with $k, m \geq1$ some positive integers. We provide sharp quantitative estimates in Gelfand-Shilov spaces for the…
In this paper, new spectral inequalities for finite combinations of eigenfunctions of anisotropic Shubin operators are presented. Given a subset $\omega$ and an energy level, we provide an explicit control of the ratio of the L 2 (R d)-norm…
We study an anisotropic version of the Shubin calculus of pseudodifferential operators on $\mathbf R^d$. Anisotropic symbols and Gabor wave front sets are defined in terms of decay or growth along curves in phase space of power type…
We study some classes of pseudo-differential operators with symbols $a$ admitting anisotropic exponential growth at infinity and we prove mapping properties for these operators on Gelfand-Shilov spaces of type S. Moreover, we deduce…
We consider time-frequency localization operators $A_a^{\varphi_1,\varphi_2}$ with symbols $a$ in the wide weighted modulation space $ M^\infty_{w}(\mathbb{R}^{2d})$, and windows $ \varphi_1, \varphi_2 $ in the Gelfand-Shilov space…
We study global regularity and spectral properties of power series of the Weyl quantisation $a^w$, where $a(x,\xi) $ is a classical elliptic Shubin polynomial. For a suitable entire function $P$, we associate two natural infinite order…
We prove quantitative spectral inequalities for the (anisotropic) Shubin operators on the whole Euclidean space, thus relating for functions from spectral subspaces associated to finite energy intervals their $L^2$-norm on the whole space…
We examine properties of Gelfand-Shilov spaces $S_s$, $S^\sigma$, $S^\sigma_s$, $\Sigma_s$, $\Sigma^\sigma$ and $\Sigma^\sigma_s$. These are spaces of smooth functions where the functions or their Fourier transforms admit sub-exponential…
In this article, we develop a calculus of Shubin type pseudodifferential operators on certain non-compact spaces, using a groupoid approach similar to the one of van Erp and Yuncken. More concretely, we consider actions of graded Lie groups…
Generalized $\mathbf{m}$-Gelfand-Shilov-Roumieu vector spaces $\mathcal{S}_{\mathbf{m}}(\mathbf{X})$ are introduced. Here $\mathbf{m} = (m^{(1)},...,m^{(n)})$, $\mathbf{X}=(X_{1},...,X_{n})$ and $m^{(1)},...,m^{(n)}$ are sequences of…
We introduce an anisotropic global wave front set of Gelfand--Shilov ultradistributions with different indices for regularity and decay at infinity. The concept is defined by the lack of super-exponential decay along power type curves in…
We introduce and study a generalization $s_{(\mu|\lambda)}$ of the Schur functions called the almost symmetric Schur functions. These functions simultaneously generalize the finite variable key polynomials and the infinite variable Schur…
We introduce a class of time-periodic Gelfand-Shilov spaces of functions on $\mathbb{T} \times \mathbb{R}^n$, where $\mathbb{T} \sim \mathbb{R} /2\pi \mathbb{Z}$ is the one-dimensional torus. We develop a Fourier analysis inspired by the…
We prove Schauder estimates for a class of non-local elliptic operators with kernel $K(y)=a(y)/|y|^{d+\sigma}$ and either Dini or H\"older continuous data. Here $0 < \sigma < 2$ is a constant and $a$ is a bounded measurable function, which…
We study Gel'fand's inverse interior spectral problem of determining a closed Riemannian manifold $(M,g)$ and a potential function $q$ from the knowledge of the eigenvalues $\lambda_j$ of the Schr\"odinger operator $-\Delta_g + q$ and the…
We consider operators of the form $\mathbf{T}=\mathbf{A^*}(V\mu)\mathbf{A}$ in $\mathbb{R}^\mathbf{N}$, where $\mathbf{A}$ is a pseudodifferential operator of order $-l$, $\mu$ is a compactly supported singular measure, order $s>0$…
We study the most general class of eigenfunction expansions for abstract normal operators with pure point spectrum in a complex Hilbert space. We find sufficient conditions for such expansions to be unconditionally convergent in spaces with…
We study asymptotic behavior of the eigenvalues of Strum--Liouville operators $Ly= -y'' +q(x)y $ with potentials from Sobolev spaces $W_2^{\theta -1}, \theta \geqslant 0$, including the non-classical case $\theta \in [0,1)$ when the…
We consider the Schr\"odinger operator with a periodic potential on quasi-1D models of armchair single-wall nanotubes. The spectrum of this operator consists of an absolutely continuous part (intervals separated by gaps) plus an infinite…