Related papers: A note on the operator window of modulation spaces
This paper is devoted to studying the boundedness of multilinear operartors and their commutators on generalized weighted Morrey spaces, which includes multilinear fractional maximal operator and multilinear fractional integral operator.…
In this paper, we introduce the notion of a characteristic operator for closable linear operators and explore their connected spectral properties via equivalence. Additionally, we develop an explicit scheme for constructing characteristic…
Real and complex norms of a linear operator acting on a normed complexified space are considered. Bounds on the ratio of these norms are given. The real and complex norms are shown to coincide for four classes of operators: 1) real linear…
We obtain a complete characterization of the norm attainment set of a bounded linear functional on a normed space, in terms of a semi-inner-product defined on the space. Motivated by this result, we further apply the concept of…
In this paper, we introduce statistical bounded set on topological vector space. Also, we consider three classes of bounded operators from topological vector spaces to ordered topological vector spaces. Moreover, we give relations between…
We consider the decomposition of bounded linear operators on Hilbert spaces in terms of functions forming frames. Similar to the singular-value decomposition, the resulting frame decompositions encode information on the structure and…
We completely characterize the boundedness of the area operators from the Bergman spaces $A^p_\alpha(\mathbb{B}_ n)$ to the Lebesgue spaces $L^q(\mathbb{S}_ n)$ for all $0<p,q<\infty$. For the case $n=1$, some partial results were…
This paper is a contribution to frame theory. Frames in a Hilbert space are generalizations of orthonormal bases. In particular, Gabor frames of $L^2(\mathbb{R})$, which are made of translations and modulations of one or more windows, are…
One can view contraction operators given by a canonical model of Sz.-Nagy and Foias as being defined by a quotient module where the basic building blocks are Hardy spaces. In this note we generalize this framework to allow the Bergman and…
This chapter offers a detailed survey on intrinsically localized frames and the corresponding matrix representation of operators. We re-investigate the properties of localized frames and the associated Banach spaces in full detail. We…
In this work, a class of semiclassical Fourier Integral Operators (FIOs) with complex phase associated to some canonical transformation of the phase space $T^*\R^d$ is constructed. Upon some general boundedness assumptions on the symbol and…
We study a composition operator on Lorentz spaces. In particular we provide necessary and sufficient conditions under which a measurable mapping induces a bounded composition operator.
We study some fundamental properties of the special affine Fourier transform (SAFT) in connection with the Fourier analysis and time-frequency analysis. We introduce the modulation space $\boldsymbol {M}^{r,s}_A$ in connection with SAFT and…
We consider the dilation property of the modulation spaces $M^{p,q}$. Let $D_\lambda:f(t)\mapsto f(\lambda t)$ be the dilation operator, and we consider the behavior of the operator norm $\|D_\lambda\|_{M^{p,q}\to M^{p,q}}$ with respect to…
In the last twenty years modulation spaces, introduced by H. G. Feichtinger in 1983, have been successfully addressed to the study of signal analysis, PDE's, pseudodifferential operators, quantum mechanics, by hundreds of contributions. In…
This paper is dedicated to the introduction in a circle of ideas and methods, which are connected with the notion of characteristic function of a non-selfadjoint operator. We start with the consideration of closed and open systems…
The purpose of the present work is to treat a new notion related to linear dynamics, which can be viewed as a "localization" of the notion of hypercyclicity. In particular, let $T$ be a bounded linear operator acting on a Banach space $X$…
In this paper we extensively investigate the class of conditionally positive definite operators, namely operators generating conditionally positive definite sequences. This class itself contains subnormal operators, $2$- and $3$-isometries…
We study Birkhoff-James orthogonality of compact (bounded) linear operators between Hilbert spaces and Banach spaces. Applying the notion of semi-inner-products in normed linear spaces and some related geometric ideas, we generalize and…
In this paper, we introduce a new class of positive linear operators that generalize the classical Bernstein operators. Specifically, we construct a sequence of operators that reproduce the logarithmic function $\ln(1+\mu+x)$, with $\mu >…