Related papers: On Schatten-von Neumann class properties of pseudo…
In this article, we explore the boundedness properties of pseudo-differential operators on radial sections of line bundles over the Poincar\'e upper half plane, even when dealing with symbols of limited regularity. We first prove the…
We consider Fourier integral operators with symbols in modulation spaces and non-smooth phase functions whose second orders of derivatives belong to certain types of modulation space. We establish continuity and Schatten-von Neumann…
We characterize the Schatten class $S^p$ of the commutator of Riesz transforms $[b,R_j]$ in $\mathbb R^n$ ($j=1,\ldots, n$) in the two weight setting for $n< p<\infty$, by introducing the condition that the symbol $b$ being in Besov spaces…
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 monograph we develop magnetic pseudodifferential theory for operator-valued and equivariant operator-valued functions and distributions from first principles. These have found plentiful applications in mathematical physics,…
We study commutators with the Riesz transforms on the Heisenberg group. The Schatten norm of these commutators is characterized in terms of Besov norms of the symbol. This generalizes the classical Euclidean results of Peller, Janson--Wolff…
We define a class of discrete operators acting on infinite, finite or periodic sequences mimicking the standard properties of pseudo-differential operators. In particular we can define the notion of order and regularity, and we recover the…
We consider a periodic pseudodifferential operator $H=(-\Delta)^l+A$ ($l>0$) in $\R^d$ which satisfies the following conditions: (i) the symbol of $H$ is smooth in $x$, and (ii) the perturbation $A$ has order smaller than $2l-1$. Under…
Given a separable unital C*-algebra A, let E denote the Banach-space completion of the A-valued Schwartz space on Rn with norm induced by the A-valued inner product $<f,g>=\int f(x)^*g(x) dx$. The assignment of the pseudodifferential…
In this monograph, we formulated the sufficient conditions of the Abel-Lidskii basis property for a sectorial operator. Having studied such an operator class, we strengthened the conditions regarding the semi-angle of the sector and…
We consider Fourier integral operators with symbols in modulation spaces and non-smooth phase functions whose second orders of derivatives belong to certain types of modulation space. We establish continuity and Schatten-von Neumann…
We show that the eigenfunctions of the self-adjoint elliptic $h-$differential operator $P_{h}(t)$ exhibits semiclassical scar phenomena on the $d-$dimensional torus, under the $\sigma$-Bruno-R\"{u}ssmann condition, instead of the…
We characterize the Schatten class membership of the canonical solution operator to $\bar\partial$ acting on $L^2(e^{-2\phi})$, where $\phi$ is a subharmonic function with $\Delta\phi$ a doubling measure. The obtained characterization is in…
Extending classical results of Janson and Peetre (1988) on the Schatten class $S^p$ membership of commutators of Riesz potentials on the Euclidean space, we obtain analogous results for commutators $[b,T]$, where…
In this paper, we introduce the concept of a pseudo weakly compact operator of order $ p $ between Banach spaces. Also we study the notion of $ p $-Dunford-Pettis relatively compact property which is in "general" weaker than the…
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…
In this review, we show how advances in the theory of magnetic pseudodifferential operators (magnetic $\Psi$DO) can be put to good use in space-adiabatic perturbation theory (SAPT). As a particular example, we extend results of [PST03] to a…
We study unconditional subsequences of the canonical basis e_rc of elementary matrices in the Schatten class S^p. They form the matrix counterpart to Rudin's Lambda(p) sets of integers in Fourier analysis. In the case of p an even integer,…
We establish the $L^p$-$L^q$-boundedness of subelliptic pseudo-differential operators on a compact Lie group $G$. Effectively, we deal with the $L^p$-$L^q$-bounds for operators in the sub-Riemmanian setting because the subelliptic classes…
We deduce trace properties for modulation spaces of Gelfand-Shilov distributions. We use these properties to show that pseudo-differential operators with amplitudes in suitable modulation spaces, agree with pseudo-differential operators of…