Related papers: Uniform stationary phase estimate with limited smo…
It is well-known that adaptive homodyne estimation of continuously varying optical phase provides superior accuracy in the phase estimate as compared to adaptive or non-adaptive static estimation. However, most phase estimation schemes rely…
We consider uniformly elliptic operators with Dirichlet or Neumann homogeneous boundary conditions on a domain $\Omega $ in ${\mathbb{R}}^N$. We consider deformations $\phi (\Omega)$ of $\Omega $ obtained by means of a locally Lipschitz…
In this paper, we establish an improved variable coefficient version of square function inequality, by which the local smoothing estimate $L^p_\alpha\rightarrow L^p$ for the Fourier integral operators satisfying cinematic curvature…
This paper studies the effects of distributed delay coupling on the dynamics in a system of non-identical coupled Stuart-Landau oscillators. For uniform and gamma delay distribution kernels, conditions for amplitude death are obtained in…
We call a function "constructible" if it has a globally subanalytic domain and can be expressed as a sum of products of globally subanalytic functions and logarithms of positively-valued globally subanalytic functions. Our main theorem…
Quantum parameter estimation is central to many fields such as quantum computation, communications and metrology. Optimal estimation theory has been instrumental in achieving the best accuracy in quantum parameter estimation, which is…
We investigate symmetric oscillators, and in particular their quantization, by employing semiclassical and quantum phase functions introduced in the context of Liouville-Green transformations of the Schr\"{o}dinger equation. For anharmonic…
We introduce an invariant phase description of stochastic oscillations by generalizing the concept of standard isophases. The average isophases are constructed as sections in the state space, having a constant mean first return time. The…
The purpose of this article is to describe the singularities of one-dimensional oscillatory integrals, whose phases have a certain singularity, in the form of an asymptotic expansion. In the case of the Laplace integral, an analogous result…
A generalized notion of oscillatory integrals that allows for inhomogeneous phase functions of arbitrary positive order is introduced. The wave front set of the resulting distributions is characterized in a way that generalizes the…
We propose a method for estimating the asymptotic phase and amplitude functions of limit-cycle oscillators using observed time series data without prior knowledge of their dynamical equations. The estimation is performed by polynomial…
Adaptive homodyne estimation of a continuously evolving optical phase using time-symmetric quantum smoothing has been demonstrated experimentally to provide superior accuracy in the phase estimate compared to adaptive or nonadaptive…
The problem of joint estimation of power spectrum and modulation from realizations of frequency modulated stationary wideband signals is considered. The study is motivated by some specific signal classes from which departures to…
In this paper we develop a theory for oscillatory integrals with complex phases. When $f:{\mathbb C}^n \to {\mathbb C}$, we evaluate this phase function on the basic character ${\rm e}(z) := e^{2\pi i x} e^{2\pi i y}$ of ${\mathbb C} \simeq…
In this paper, we first generalize the Fresnel integrals by changing of a path for integration in the proof of the Fresnel integrals by Cauchy's integral theorem. Next, according to oscillatory integral, we also obtain further…
In this paper we establish sharp estimates (up to logarithmic losses) for the multilinear oscillatory integral operator studied by Phong, Stein, and Sturm and Carbery and Wright on any product $\prod_{j=1}^d L^{p_j}(\mathbb R)$ with each…
We present and compare three generically applicable signal processing methods for periodic orbit quantization via harmonic inversion of semiclassical recurrence functions. In a first step of each method, a band-limited decimated periodic…
We consider the continuous-time version of our recently proposed quantum theory of optical temporal phase and instantaneous frequency [Tsang, Shapiro, and Lloyd, Phys. Rev. A 78, 053820 (2008)]. Using a state-variable approach to…
Oscillatory systems arise in the different science fields. Complex mathematical formulations with differential equations have been proposed to model the dynamics of these systems. While they have the advantage of having a direct…
We study oscillatory integrals in several variables with analytic, smooth, or $C^k$ phases satisfying a nondegeneracy condition attributed to Varchenko. With only real analytic methods, Varchenko's estimates are rediscovered and…