arXiv subjects

Nenad Teofanov

Publications and source records attributed to Nenad Teofanov.

At least 19 recordsLinked to original sources

arXiv2026

Continuity properties of the Laguerre operator and its propagator

We study the well-posedness of a Cauchy problem associated with the general form of the Laguerre operator and relate it to the corresponding global problem for the harmonic oscillator. To this end, we carry out a detailed analysis of the continuity properties of the associated propagator. Furthermore, we establish connections between several integral transforms, including the fractional Fourier transform and the fractional Hankel transform. Our results highlight the role of Pilipović spaces on positive orthants when studying problems involving the Laguerre operator.

math.AP↗

arXiv2026

Compactness for pseudo-differential and Toeplitz operators on modulation spaces

We deduce various norm equivalences, and convolution estimates for the modulation space $M^{\sharp ,q}_{(ω)}$ consisting of all $f\in M^{\infty ,q}_{(ω)}$ such that $|V_ϕf \cdot ω|$ satisfies a mild vanishing condition at infinity. We prove that $M^{\sharp ,q}_{(ω)}$ is the completion of the Gelfand-Shilov space $Σ_1$ under the $M^{\infty ,q}_{(ω)}$ norm. We use these results to deduce compactness for $Ψ$DO $\op (\mathfrak a )$, with $\mathfrak a \in M^{\sharp ,q}_{(ω)}$, $0<q\le 1$, when acting on a broad family of modulation spaces.

math.FA↗

arXiv2025

Gelfand-Shilov spaces for extended Gevrey regularity

We consider spaces of smooth functions obtained by relaxing Gevrey-type regularity and decay conditions. It is shown that these classes fit well within the general framework of the weighted matrices approach to ultradifferentiable functions. We examine equivalent ways of introducing Gelfand-Shilov spaces related to the extended Gevrey regularity and derive their nuclearity. In addition to the Fourier transform invariance property, we present their corresponding symmetric characterizations. Finally, we consider some time-frequency representations of the introduced classes of ultradifferentiable functions.

math.FA↗

arXiv2025

Norm estimates for a broad class of modulation spaces, and continuity of Fourier type operators

Let $\mathscr B$ be a normal quasi-Banach function space with respect to $r_0 \in (0,1]$ and $v_0$, $ω$ be $v$-moderate, and let $r\in [r_0,\infty ]$. Then we prove that $f$ belongs to the modulation space $M(ω,\mathscr B )$, iff $V_ϕf$ belongs to the Wiener amalgam space $W ^r(ω,\mathscr B )$, and $$ \| f \| _{M(ω, \mathscr B)} \asymp \| V _ϕf \, ω\| _{\mathscr B} \asymp \| V _ϕf\| _{W ^r(ω, \mathscr B)}. $$ We also use the results to deduce continuity for pseudo-differential operators with symbols in weighted $M^{\infty,r_0}$-spaces, with $r_0\le 1$, when acting on $M(ω,\mathscr B )$-spaces.

math.FA↗

arXiv2024

Ultradifferentiable functions via the Laguerre operator

We define and characterize ultradifferentiable functions and their corresponding ultradistributions on $\RR^d_+$ using iterates of the Laguerre operator. The characterization is based on decay or growth conditions of the coefficients in their Laguerre series expansion. We apply our results to establish an isomorphism between subspaces of Pilipović spaces on $\RR^d$, and the spaces of ultradifferentiable functions on $\RR^d_+$.

math.FA↗

arXiv2024

On the iterates of the Laguerre operator

We use the iterates of the Laguerre operator to introduce Pilipović spaces on positive orthants. It is shown that such spaces coincide with $G-$type spaces $g_α^α(\mathbb{R}^d_+)$ and $G_α^α(\mathbb{R}^d_+)$, when $α> 1$, and $α\geq 1$, respectively. However, in contrast to $G$-type spaces, Pilipović spaces on positive orthants are nontrivial below the critical index $α= 1$. We also remark that there is a natural isomorphism between subspaces of Pilipović spaces on $\mathbb{R}^d$ consisting of even functions, and Pilipović spaces on positive orthants.

math.FA↗

arXiv2024

An introduction to extended Gevrey regularity

Gevrey classes are the most common choice when considering the regularities of smooth functions that are not analytic. However, in various situations, it is important to consider smoothness properties that go beyond Gevrey regularity, for example when initial value problems are ill-posed in Gevrey settings. Extended Gevrey classes provide a convenient framework for studying smooth functions that possess weaker regularity than any Gevrey function. Since the available literature on this topic is scattered, our aim is to provide an overview to extended Gevrey regularity, highlighting its most important features. Additionally, we consider related dual spaces of ultradistributions and review some results on micro-local analysis in the context of extended Gevrey regularity. We conclude the paper with a few selected applications that may motivate further study of the topic.

math.AP↗

arXiv2024

Dilation estimates for Wiener amalgam spaces of Orlicz type

We extend dilation properties of Wiener amalgam spaces when the local and global componenets are Lebesgue spaces to a more general setting of Orlicz spaces. We recover the result of Cordero and Nicola when restricted to Lebesgue spaces. In addition, we prove continuity of the Zak transform on Wiener amalgam spaces with Orlicz spaces as their local components.

math.FA↗

arXiv2024

Almost diagonalization of $Ψ$DO's over various generalized function spaces

Inductive and projective type sequence spaces of sub- and super-exponential growth, and the corresponding inductive and projective limits of modulation spaces are considered as a framework for almost diagonalization of pseudo-differential operators. Moreover, recent results of the first author and B. Prangoski related to the almost diagonalization of pseudo-differential operators in the context of Hörmander metrics are reviewed.

math.FA↗

arXiv2024

Band-limited wavelets beyond Gevrey regularity

It is known that a smooth function of exponential decay at infinity can not be an orthonormal wavelet. Dziubański and Hernández constructed smooth orthonormal wavelets of Gevrey type subexponential decay. We weaken the Gevrey type decay and construct orthonormal wavelets of subexponential decay related to the so-called extended Gevrey classes. The virtue of our construction is that prescise asymptotics of functions from such classes can be given in terms of the Lambert $W$ function.

math.FA↗

arXiv2022

Extended Gevrey regularity via weighted matrices

The main aim of this paper is to compare two recent approaches for investigating the interspace between the union of Gevrey spaces $\mathcal G_t (U)$ and the space of smooth functions $C^{\infty}(U)$. The first approach in the style of Komatsu is based on the properties of two parameter sequences $M_p=p^{τp^σ}$, $τ>0$, $σ>1$. The other one uses weight matrices defined by certain weight functions. We prove the equivalence of the corresponding spaces in the Beurling case by taking projective limits with respect to matrix parameters, while in the Roumieu case we need to consider a larger space then the one obtained as the inductive limit of extended Gevrey classes.

math.FA↗

arXiv2022

Short-time Fourier transform of the pointwise product of two functions with application to the nonlinear Schrödinger equation

We show that the short-time Fourier transform of the pointwise product of two functions $f$ and $h$ can be written as a suitable product of the short-time Fourier transforms of $f$ and $h$. The same result is then shown to be valid for the Wigner wave-packet transform. We study the main properties of the new products. We then use these products to derive integro-differential equations on the time-frequency space equivalent to, and generalizing, the cubic nonlinear Schrödinger equation. We also obtain the Weyl-Wigner-Moyal equation satisfied by the Wigner-Ville function associated with the solution of the nonlinear Schrödinger equation. The new equation resembles the Boltzmann equation.

math-ph↗

arXiv2022

An excursion to multiplications and convolutions on modulation spaces

We give a self-contained introduction to (quasi-)Banach modulation spaces of ultradistributions, and review results on boundedness for multiplications and convolutions for elements in such spaces. Furthermore, we use these results to study the Gabor product. As an example, we show how it appears in a phase-space formulation of the nonlinear cubic Schrödinger equation.

math.FA↗

arXiv2022

Continuous frames in tensor product Hilbert spaces, localization operators and density operators

Continuous frames and tensor products are important topics in theoretical physics. This paper combines those concepts. We derive fundamental properties of continuous frames for tensor product of Hilbert spaces. This includes, for example, the consistency property, i.e. preservation of the frame property under the tensor product, and the description of the canonical dual tensors by those on the Hilbert space level. We show the full characterization of all dual systems for a given continuous frame, a result interesting by itself, and apply this to dual tensor frames. Furthermore, we discuss the existence on non-simple tensor product (dual) frames. Continuous frame multipliers and their Schatten class properties are considered in the context of tensor products. In particular, we give sufficient conditions for obtaining partial trace multipliers of the same form, which is illustrated with examples related to short-time Fourier transform and wavelet localization operators. As an application, we offer an interpretation of a class of tensor product continuous frame multipliers as density operators for bipartite quantum states, and show how their structure can be restricted to the corresponding partial traces.

math.FA↗

arXiv2021

Wilson bases and ultradistributions

We give a characterization of Gelfand-Shilov type spaces of test functions and their dual spaces of tempered ultradistributions by the means of Wilson bases of exponential decay. We offer two different proofs, and extend known results to the Roumieu case.

math.FA↗

arXiv2021

Some remarks on analytic pseudodifferential operators

We report some recent results on analytic pseudodifferential operators, also known as Wick operators. An important tool in our study is the Bargmann transform which provides a coupling between the classical (real) and analytic pseudodifferential calculus. Since the Bargmann transform of Hermite functions gives rise to formal power series in the complex domain, the results are formulated in terms of the Bargmann images of Pilipović spaces.

math.AP↗

arXiv2021

Pseudo-differential operators with isotropic symbols, Wick and anti-Wick operators, and hypoellipticity

We study the link between pseudo-differential operators and Wick operators via the Bargmann transform. We deduce a formula for the symbol of the Wick operator in terms of the short-time Fourier transform of the Weyl symbol. This gives characterizations of Wick symbols of pseudo-differential operators of Shubin type and of infinite order, and results on composition. We prove a series expansion of Wick operators in anti-Wick operators which leads to a sharp Gårding inequality and transition of hypoellipticity between Wick and and Shubin symbols. Finally we show continuity results for anti-Wick operators, and estimates for the Wick symbols of anti-Wick operators.

math.FA↗

arXiv2020

Boundary values in ultradistribution spaces related to extended Gevrey regularity

Following the well-known theory of Beurling and Roumieu ultradistributions, we investigate new spaces of ultradistributions as dual spaces of test functions which correspond to associated functions of logarithmic-type growth at infinity. In the given framework we prove that boundary values of analytic functions with the corresponding logarithmic growth rate towards the real domain are ultradistributions. The essential condition for that purpose, condition $(M.2)$ in the classical ultradistribution theory, is replaced by the new one, $\widetilde{(M.2)}$. For that reason, new techniques were performed in the proofs. As an application, we discuss the corresponding wave front sets.

math.FA↗