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An extension of localization operators
We review at first the role of localization operators as a meeting point of three different areas of research, namely: signal analysis, quantization...
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Wigner analysis of fourier integral operators with symbols in the Shubin classes
We study the decay properties of Wigner kernels for Fourier integral operators of types I and II. The symbol spaces that allow a nice decay of these...
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A sharp Hörmander estimate for multi-parameter and multi-linear Fourier multiplier operators
In this paper, we investigate the Hörmander type theorems for the multi-linear and multi-parameter Fourier multipliers. When the multipliers are...
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On weak (measure valued)–strong uniqueness for Navier–Stokes–Fourier system with Dirichlet boundary condition
In this article, our goal is to define a measure valued solution of compressible Navier–Stokes–Fourier system for a heat conducting fluid with...
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Fourier Series and Gauss Sums
The basic functions that we will be concerned with in this chapter are for $$n...
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The 2-D Hyper-complex Gabor quadratic-phase Fourier transform and uncertainty principles
In this paper, we present a novel integral transform known as the 2-D Hyper-complex(quaternion) Gabor quadratic-phase Fourier transform (Q-GQPFT),...
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Pareto Adaptive Robust Optimality via a Fourier–Motzkin Elimination lens
We formalize the concept of Pareto Adaptive Robust Optimality (PARO) for linear two-stage Adaptive Robust Optimization (ARO) problems, with fixed...
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Dimensional Reduction by Fourier Analysis of a Stokes-Darcy Fracture Model
We consider a Stokes flow along a thin fracture coupled to a Darcy flow in the surrounding matrix domain. In order to derive a dimensionally reduced...
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Fourier restriction for smooth hyperbolic 2-surfaces
We prove Fourier restriction estimates by means of the polynomial partitioning method for compact subsets of any sufficiently smooth hyperbolic...
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A Family of Fractal Fourier Restriction Estimates with Implications on the Kakeya Problem
In a recent paper, Du and Zhang (Ann Math 189:837–861, 2019) proved a fractal Fourier restriction estimate and used it to establish the sharp
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Inner Product and Fourier Expansion
In this chapter, we consider a scalar-valued binary operation on a linear space called an inner product. It leads to the concepts of the length of a...
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Low regularity a priori estimate for KDNLS via the short-time Fourier restriction method
In this article, we consider the kinetic derivative nonlinear Schrödinger equation (KDNLS), which is a one-dimensional nonlinear Schrödinger equation...
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Relation between Fourier series and Wiener algebras
New relations between the Banach algebras of absolutely convergent Fourier integrals of complex-valued measures of Wiener and various issues of...
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A solution for reducing the degree of polynomial composition functions using Faà di Bruno’s formula and Fourier transform
Various studies concerning reducing the degree of order for nonlinear differential equations have been carried out. Yet, reducing the specified...
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Restriction Theorem Fails for the Fourier–Hermite Transform Associated with the Normalized Hermite Polynomials with Respect to a Discrete Surface
The aim of the article is to show the invalidity of the Strichartz estimate for the free Schrödinger equation associated with the Ornstein–Uhlenbeck...