Related papers: Mutual estimates of time-frequency representations…
Heisenberg's uncertainty principle implies fundamental constraints on what properties of a quantum system can we simultaneously learn. However, it typically assumes that we probe these properties via measurements at a single point in time.…
We develop an interpretable and learnable Wigner-Ville distribution that produces a super-resolved quadratic signal representation for time-series analysis. Our approach has two main hallmarks. First, it interpolates between known…
In this manuscript, we introduce the quadratic--phase Fourier--Bessel transform and develop its foundational properties, including continuity, the Riemann--Lebesgue lemma, reversibility, and Parseval's identity. We define the associated…
Using energy methods, we prove some power-law and exponential decay estimates for classical and nonlocal evolutionary equations. The results obtained are framed into a general setting, which comprise, among the others, equations involving…
This is the second part of a series of four articles on weighted norm inequalities, off-diagonal estimates and elliptic operators. We consider a substitute to the notion of pointwise bounds for kernels of operators which usually is a…
Motivated by statistical analysis of latent factor models for high-frequency financial data, we develop sharp upper bounds for the spectral norm of the realized covariance matrix of a high-dimensional It\^o semimartingale with possibly…
The construction of numerical value scales (or priority values) is a recurrent topic in decision-aiding research. However, in real contexts, uncertainty and limited cognitive precision often lead decision-makers to provide interval…
We establish the $L_p$-solvability for time fractional parabolic equations when coefficients are merely measurable in the time variable. In the spatial variables, the leading coefficients locally have small mean oscillations. Our results…
We study the process of dispersion of low-regularity solutions to the Schr\"odinger equation using fractional weights (observables). We give another proof of the uncertainty principle for fractional weights and use it to get a lower bound…
This brief note wants to bring to attention that the formulation of physically reasonable initial-boundary value problems for wave equations in Lorentzian space-times is not unique, i.e., that there are inequivalent such formulations that…
This paper derives a new directional uncertainty principle for quaternion valued functions subject to the quaternion Fourier transformation. This can be generalized to establish directional uncertainty principles in Clifford geometric…
We extend the classical Hardy-Sobolev-Poincare-Wirtinger inequalities from the ordinary Lebesgue-Riesz spaces into the Grand Lebesgue ones, with exact constants evaluation.
A time-varying empirical spectral process indexed by classes of functions is defined for locally stationary time series. We derive weak convergence in a function space, and prove a maximal exponential inequality and a…
In this paper we obtain the non-asymptotic norm estimations of Besov's type between the norms of a functions in different Bilateral Grand Lebesgue spaces (BGLS). We also give some examples to show the sharpness of these inequalities.
We investigate the Hilbert transform and the maximal operator along a class of variable non-flat polynomial curves $(P(t),u(x)t)$ with measurable $u(x)$, and prove uniform $L^p$ estimates for $1<p<\infty$. In particular, via the change of…
We prove duality estimates for time-fractional and more general subdiffusion problems. An important example is given by subdiffusive porous medium type equations. Our estimates can be used to prove uniqueness of weak solutions to such…
Dispersive and Strichartz estimates for solutions to general strictly hyperbolic partial differential equations with constant coefficients are considered. The global time decay estimates of $L^p-L^q$ norms of propagators are obtained, and…
In this paper we consider an SPDE where the leading term is a second order operator with periodic boundary conditions, coefficients which are measurable in $(t,\omega)$, and H\"older continuous in space. Assuming stochastic parabolicity…
We develop a weighted mixed-norm $L_q(L_p)$-estimates for solutions to fractional evolution equations of the form \[ \partial_t^\alpha w(t,x) = \phi(\Delta) w(t,x) + h(t,x), \quad w(0,\cdot) = w_0, \quad t > 0, \; x \in \mathbb{R}^d, \]…
A comprehensive uncertainty estimation is vital for the precision program of the LHC. While experimental uncertainties are often described by stochastic processes and well-defined nuisance parameters, theoretical uncertainties lack such a…