Related papers: Fourier integral operators on Orlicz modulation sp…
This article gives explicit integral formulas for the so-called generalized metaplectic operators, i.e. Fourier integral operators (FIOs) of Schr\"odinger type, having a symplectic matrix as canonical transformation. These integrals are…
We generalize von Neumann's well-known trace inequality, as well as related eigenvalue inequalities for hermitian matrices, to Schatten-class operators between complex Hilbert spaces of infinite dimension. To this end, we exploit some…
Here, the composition operators on Orlicz spaces with finite ascent and descent as well as infinite ascent and descent are characterized.
In this paper, we give the necessary and sufficient conditions for the boundedness of fractional integral operators on the modulation spaces.
We link Sogge's type $L^p$-estimates for eigenfunctions of the Laplacian on compact manifolds with the problem of providing criteria for the $r$-nuclearity of Fourier integral operators. The classes of Fourier integral operators…
Let $f \in M_+(\mathbb{R}_+)$, the class of nonnegative, Lebesgure-measurable functions on $\mathbb{R}_+=(0, \infty)$. We deal with integral operators of the form \[ (T_Kf)(x)=\int_{\mathbb{R}_+}K(x,y)f(y)\, dy, \quad x \in \mathbb{R}_+, \]…
We establish certain square function estimates for a class of oscillatory integral operators with homogeneous phase functions. These results are employed to deduce a refinement of a previous result of Mockenhaupt Seeger and Sogge…
We extend Feichtinger's minimality property on smallest non-trivial time-frequency shift invariant Banach spaces, to the quasi-Banach case. Analogous properties are deduced for certain matrix classes. We use these results to prove that…
In this paper we introduce the Schatten class of operators and the Berezin transform of operators in the quaternionic setting. The first topic is of great importance in operator theory but it is also necessary to study the second one…
We investigate spaces of operators which are invariant under translations or modulations by lattices in phase space. The natural connection to the Heisenberg module is considered, giving results on the characterisation of such operators as…
In the present paper we provide some equivalent conditions for composition operators to have shadowing property on Orlicz space. Also, we obtain that for the composition operators on Orlicz spaces the notions of generalized hyperbolicity…
Generalized Fourier integral operators (FIOs) acting on Colombeau algebras are defined. This is based on a theory of generalized oscillatory integrals (OIs) whose phase functions as well as amplitudes may be generalized functions of…
We study integral operators $\mathcal{L}u(x)=\int_{\mathbb{R^N}}\psi(u(x)-u(y))J(x-y)\,dy$ of the type of the fractional $p$-Laplacian operator, and the properties of the corresponding Orlicz and Sobolev-Orlicz spaces. In particular we show…
We study a specific class of Fourier integral operators characterized by symbols belonging to the multi-parameter H\"ormander class $\mathbf{S}^m(\R^{ n_1} \times \R^{ n_2} \times \cdots \times \R^{n_d} )$, where $n= n_1 + n_2 +\cdots +…
Self-adjoint Schr\"odinger operators with $\delta$ and $\delta'$-potentials supported on a smooth compact hypersurface are defined explicitly via boundary conditions. The spectral properties of these operators are investigated, regularity…
We construct a one-parameter family of algebras consisting of Fourier integral operators. We derive boundedness results, composition rules, and the spectral invariance of this class of operators. The operator algebra is defined by the decay…
Boundedness results for multilinear pseudodifferential operators on products of modulation spaces are derived based on ordered integrability conditions on the short-time Fourier transform of the operators' symbols. The flexibility and…
We obtain a number of explicit estimates for quasi-norms of pseudo-differential operators in the Schatten-von Neumann classes $S_q$ with $0<q\le 1$. The estimates are applied to derive semi-classical bounds for operators with smooth or…
In this paper we focus on the almost-diagonalization properties of $\tau$-pseudodifferential operators using techniques from time-frequency analysis. Our function spaces are modulation spaces and the special class of Wiener amalgam spaces…
We introduce theta-functions of VOA-modules and show that the space spanned by them has a modular invariance property.