Journal of Functional Analysis最新文献

英文中文

Piecewise linear and step Fourier multipliers for modulation spaces

IF 1.7 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2024-12-09 DOI: 10.1016/j.jfa.2024.110795

Hans G. Feichtinger , Ferenc Weisz

This note significantly extends various earlier results concerning Fourier multipliers of modulation spaces. It combines not so widely known characterizations of pointwise multipliers of Wiener amalgam spaces with novel geometric ideas and a new approach to piecewise linear functions belonging to the Fourier algebra. Thus the paper provides two original types of results.

On the one hand we establish results for step functions (i.e. piecewise constant, bounded functions), which are multipliers on the modulation spaces

(M_{ω}^{p, q} (R^{d}), {‖ \cdot ‖}_{M_{ω}^{p, q}})

with

1 < p < \infty

, fixed. Instead of regular patterns with a discrete subgroup structure we demonstrate that there is a significant freedom in the choice of the domains of constant values. In particular for higher dimensions (i.e.,

d \geq 2

), this widens the scope of possible multipliers very much. Adding some geometric considerations we show that the step functions, which arise as nearest neighborhood interpolation (using the so-called Voronoi cells) from roughly well-spread sets with bounded values define Fourier multipliers in this range, with uniform control for large families of such sets. Parameterized families of lattices are just simple special cases.

In the second part of the paper we aim at sufficient conditions for piecewise linear Fourier multipliers, with uniform estimates for the range

p \in [1, \infty]

(and independent from q and s). These results are based on the control on the Fourier algebra norm of (oblique) triangular functions on

R

. This result is of independent interest, as it provides new sufficient conditions for the membership of piecewise linear functions (with irregular nodes) in the modulation space

M^{1} (R^{d})

, also known as the Segal algebra

S_{0} (R^{d})

(see [6] and [25]).

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引用次数: 0

Some uniformization problems for a fourth order conformal curvature

IF 1.7 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2024-12-09 DOI: 10.1016/j.jfa.2024.110791

Sanghoon Lee

In this paper, we establish the existence of conformal deformations that uniformize fourth order curvature on 4-dimensional Riemannian manifolds with positive conformal invariants. Specifically, we prove that any closed, compact Riemannian manifold with positive Yamabe invariant and total Q-curvature can be conformally deformed into a metric with positive scalar curvature and constant Q-curvature. For a Riemannian manifold with umbilic boundary, positive first Yamabe invariant and total

(Q, T)

-curvature, it is possible to deform it into two types of Riemannian manifolds with totally geodesic boundary and positive scalar curvature. The first type satisfies

Q \equiv constant, T \equiv 0

while the second type satisfies

Q \equiv 0, T \equiv constant

引用次数: 0

On the concentration of the Fourier coefficients for products of Laplace-Beltrami eigenfunctions on real-analytic manifolds

IF 1.7 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2024-12-09 DOI: 10.1016/j.jfa.2024.110792

Philippe Charron, François Pagano

On a closed analytic manifold

(M, g)

, let

ϕ_{i}

be the eigenfunctions of

Δ_{g}

with eigenvalues

λ_{i}^{2}

and let

f : = \prod ϕ_{k_{j}}

be a finite product of Laplace-Beltrami eigenfunctions. We show that

{〈 f, ϕ_{i} 〉}_{L^{2} (M)}

decays exponentially as soon as

λ_{i} > C \sum λ_{k_{j}}

for some constant C depending only on M. Moreover, by using a lower bound on

{‖ f ‖}_{L^{2} (M)}

, we show that 99% of the

L^{2}

-mass of f can be recovered using only finitely many Fourier coefficients.

引用次数: 0

Weak solutions to a hyperbolic-elliptic problem

IF 1.7 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2024-12-09 DOI: 10.1016/j.jfa.2024.110798

Seonghak Kim

We prove the existence of infinitely many local-in-time weak solutions to the initial-boundary value problem for a class of hyperbolic-elliptic equations in dimension

n \geq 2

when the range of the magnitude of the initial spatial gradient overlaps with the unstable elliptic regime. Such solutions are extracted from the method of convex integration in a Baire category setup; they are smooth outside the phase mixing zone that is determined by a modified hyperbolic evolution, continuous on the space-time domain, and Lipschitz continuous in terms of the spatial variables.

引用次数: 0

Orthogonal factors of operators on the Rosenthal Xp,w spaces and the Bourgain-Rosenthal-Schechtman Rωp space

IF 1.7 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2024-12-06 DOI: 10.1016/j.jfa.2024.110802

Konstantinos Konstantos , Pavlos Motakis

For

1 < p < \infty

, we show that the Rosenthal

X_{p, w}

spaces and the Bourgain-Rosenthal-Schechtman

R_{ω}^{p}

space have the factorization property and the primary factorization property.

引用次数: 0

Entanglement-assisted classical capacities of some channels acting as radial multipliers on fermion algebras

IF 1.7 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2024-12-06 DOI: 10.1016/j.jfa.2024.110790

Cédric Arhancet

We investigate a new class of unital quantum channels on

M_{2^{k}}

, acting as radial multipliers when we identify the matrix algebra

M_{2^{k}}

with a finite-dimensional fermion algebra. Our primary contribution lies in the precise computation of the (optimal) rate at which classical information can be transmitted through these channels from a sender to a receiver when they share an unlimited amount of entanglement. Our approach relies on new connections between fermion algebras with the n-dimensional discrete hypercube

{- 1, 1}^{n}

. Significantly, our calculations yield exact values applicable to the operators of the fermionic Ornstein-Uhlenbeck semigroup. This advancement not only provides deeper insights into the structure and behaviour of these channels but also enhances our understanding of Quantum Information Theory in a dimension-independent context.

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引用次数: 0

Time-dependent flows and their applications in parabolic-parabolic Patlak-Keller-Segel systems Part I: Alternating flows

IF 1.7 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2024-12-06 DOI: 10.1016/j.jfa.2024.110786

Siming He

We consider the three-dimensional parabolic-parabolic Patlak-Keller-Segel equations (PKS) subject to ambient flows. Without the ambient fluid flow, the equation is super-critical in three-dimension and has finite-time blow-up solutions with arbitrarily small

L^{1}

-mass. In this study, we show that a family of time-dependent alternating shear flows, inspired by the clever ideas of Tarek Elgindi [39], can suppress the chemotactic blow-up in these systems.

引用次数: 0

Highly singular (frequentially sparse) steady solutions for the 2D Navier–Stokes equations on the torus 环面上二维Navier-Stokes方程的高度奇异（频繁稀疏）稳态解

IF 1.7 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2024-11-22 DOI: 10.1016/j.jfa.2024.110761

Pierre Gilles Lemarié-Rieusset

We construct non-trivial steady solutions in

H^{- 1}

for the 2D Navier–Stokes equations on the torus. In particular, the solutions are not square integrable, so that we have to introduce a notion of special (non square integrable) solutions.

我们构造了环面上二维Navier-Stokes方程在H−1中的非平凡稳定解。特别地，解不是平方可积的，所以我们必须引入一个特殊（非平方可积）解的概念。

引用次数: 0

Normalized ground states for Schrödinger equations on metric graphs with nonlinear point defects 具有非线性点缺陷的度量图上Schrödinger方程的归一化基态

IF 1.7 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2024-11-22 DOI: 10.1016/j.jfa.2024.110760

Filippo Boni , Simone Dovetta , Enrico Serra

We investigate the existence of normalized ground states for Schrödinger equations on noncompact metric graphs in presence of nonlinear point defects, described by nonlinear δ-interactions at some of the vertices of the graph. For graphs with finitely many vertices, we show that ground states exist for every mass and every

L^{2}

-subcritical power. For graphs with infinitely many vertices, we focus on periodic graphs and, in particular, on

Z

-periodic graphs and on a prototypical

Z^{2}

-periodic graph, the two–dimensional square grid. We provide a set of results unravelling nontrivial threshold phenomena both on the mass and on the nonlinearity power, showing the strong dependence of the ground state problem on the interplay between the degree of periodicity of the graph, the total number of point defects and their dislocation in the graph.

研究了存在非线性点缺陷的非紧度量图上Schrödinger方程的归一化基态的存在性，这些缺陷由图中某些顶点的非线性δ-相互作用描述。对于有有限多个顶点的图，我们证明了每个质量和每个l2次临界功率都存在基态。对于具有无限多个顶点的图，我们关注周期图，特别是z -周期图和典型的z2 -周期图，二维方形网格。我们提供了一组关于质量和非线性功率的非琐琐性阈值现象的结果，显示了基态问题与图中周期性程度、点缺陷总数及其位错之间的相互作用的强烈依赖性。

引用次数: 0

Bounds for the kernel of the (κ,a)-generalized Fourier transform 广义傅里叶变换（κ,a）核函数的界

IF 1.7 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2024-11-22 DOI: 10.1016/j.jfa.2024.110755

Hendrik De Bie , Pan Lian , Frederick Maes

In this paper, we study the pointwise bounds for the kernel of the

(κ, a)

-generalized Fourier transform with

κ \equiv 0

, introduced by Ben Saïd, Kobayashi and Ørsted. We present explicit formulas for the case

a = 4

, which show that the kernels can exhibit polynomial growth. Subsequently, we provide a polynomial bound for the even dimensional kernel for this transform, focusing on the cases with finite order. Furthermore, by utilizing an estimation for the Prabhakar function, it is found that the

(0, a)

-generalized Fourier kernel is bounded by a constant when

a > 1

and

m \geq 2

, except within an angular domain that diminishes as

a \to \infty

. As a byproduct, we prove that the

(0, 2^{ℓ} / n)

-generalized Fourier kernel is uniformly bounded, when

m = 2

and

ℓ, n \in N

在本文中，我们研究了Ben Saïd， Kobayashi和Ørsted引入的(κ,a)-广义傅里叶变换（κ≡0）核的点向界。我们给出了a=4情况下的显式公式，表明核可以呈现多项式增长。随后，我们给出了该变换的偶维核的多项式界，重点讨论了有限阶的情况。进一步，通过对Prabhakar函数的估计，我们发现(0,a)-广义傅里叶核在a>；1和m≥2时被一个常数限定，除了在角域内随着a→∞而减小。作为副产物，我们证明了(0,2 r /n)-广义傅里叶核是一致有界的，当m=2且r，n∈n。

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引用次数: 0

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