Classical Analysis and ODEs Papers (@ClassicalODEs) | Aguea

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Classical Analysis and ODEs Papers @ClassicalODEs

11h

Local convergence of Sussmann's infinite product for analytic vector fields Jérémy Le Borgne, Frédéric Marbach arxiv.org/abs/2606.14500 [𝚖𝚊𝚝𝚑.𝙲𝙰 𝚖𝚊𝚝𝚑.𝙾𝙲]

Local convergence of Sussmann's infinite product for analytic...

In 1986, Sussmann proposed an expansion of the Chen series as an infinite product of exponentials of Hall basis elements multiplied by coefficients defined through a simple induction. He proved...

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Classical Analysis and ODEs Papers @ClassicalODEs

11h

lᵖ-Lq boundedness of sequence-to-function Hardy-Littlewood-Pólya-type operators Jianjun Jin arxiv.org/abs/2606.13976 [𝚖𝚊𝚝𝚑.𝙲𝙰]

$l^{p}-L^{q}$ boundedness of sequence-to-function...

In this paper we deal with the boundedness of certain generalized sequence-to-function Hardy-Littlewood-Pólya-type operators. We completely characterize the $l^{p}-L^{q}$ boundedness of these...

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Classical Analysis and ODEs Papers @ClassicalODEs

12h

A remark on Chebyshev rational functions, multipoint Padé approximants and Noise Maxim Derevyagin, Max Meynig arxiv.org/abs/2606.13965 [𝚖𝚊𝚝𝚑.𝙲𝙰 𝚑𝚎𝚙-𝚝𝚑 𝚖𝚊𝚝𝚑-𝚙𝚑 𝚖𝚊𝚝𝚑.𝙲𝚅]

A remark on Chebyshev rational functions, multipoint Padé...

Motivated by the recent interest in multipoint Padé approximants in the physics community, we discuss Chebyshev rational functions and show how they give rise to multipoint Padé approximants...

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Classical Analysis and ODEs Papers @ClassicalODEs

12h

Almost everywhere divergence of Cesaro means of subsequences of Walsh–Paley Fourier partial sums Istvan Blahota, Gyorgy Gat arxiv.org/abs/2606.13879 [𝚖𝚊𝚝𝚑.𝙲𝙰]

Almost everywhere divergence of Cesaro means of subsequences of...

We prove an almost everywhere divergence theorem for Cesàro means of subsequences of partial sums of Walsh--Fourier series. More precisely, we show that there exists a strictly increasing...

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Classical Analysis and ODEs Papers @ClassicalODEs

Jun 12

Dimension-free Markov–Bernstein inequalities for product measures Egor Kosov arxiv.org/abs/2606.13575 [𝚖𝚊𝚝𝚑.𝙲𝙰 𝚖𝚊𝚝𝚑.𝙵𝙰 𝚖𝚊𝚝𝚑.𝙿𝚁]

Dimension-free Markov--Bernstein inequalities for product measures

We study dimension-free Markov--Bernstein inequalities for polynomials with respect to product probability measures. In the Gaussian case, for $p\ge4$, we prove that \[ \|\nabla...

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Classical Analysis and ODEs Papers @ClassicalODEs

Jun 12

Pathwise integration beyond Young via Faber–Schauder energy spaces Donghan Kim arxiv.org/abs/2606.13331 [𝚖𝚊𝚝𝚑.𝙲𝙰 𝚖𝚊𝚝𝚑.𝙵𝙰 𝚖𝚊𝚝𝚑.𝙿𝚁]

Pathwise integration beyond Young via Faber--Schauder energy spaces

We develop a pathwise integration theory based on Faber--Schauder energy spaces. The approach replaces the classical Hölder--Young and finite-variation Young conditions by dyadic summability...

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Classical Analysis and ODEs Papers @ClassicalODEs

Jun 12

Quantitative flatness and obstructions in Fourier analysis Jonathan M. Fraser arxiv.org/abs/2606.13170 [𝚖𝚊𝚝𝚑.𝙲𝙰 𝚖𝚊𝚝𝚑.𝙳𝙶 𝚖𝚊𝚝𝚑.𝙳𝚂 𝚖𝚊𝚝𝚑.𝙵𝙰 𝚖𝚊𝚝𝚑.𝙼𝙶]

Quantitative flatness and obstructions in Fourier analysis

Three important problems in Fourier analysis are the Fourier restriction problem, the $L^p$-improving problem, and the Fourier decay problem. Positive results for any of these problems require a...

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Classical Analysis and ODEs Papers @ClassicalODEs

Jun 12

On Almgren's Multiple-valued Functions of Class 1 Nicolau S. Aiex arxiv.org/abs/2606.13002 [𝚖𝚊𝚝𝚑.𝙲𝙰]

On Almgren's Multiple-valued Functions of Class 1

We prove that all reasonable definitions of multiple-valued functions with continuous derivatives are equivalent, which eliminates inconsistencies in the literature. As an intermediate result we...

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Classical Analysis and ODEs Papers @ClassicalODEs

Jun 12

The (local) geometry of oscillatory integrals on manifolds: Dimension three Song Dai, Liuwei Gong, Shaoming Guo arxiv.org/abs/2606.12927 [𝚖𝚊𝚝𝚑.𝙲𝙰 𝚖𝚊𝚝𝚑.𝙳𝙶]

The (local) geometry of oscillatory integrals on manifolds: Dimension three

Sogge studied Kakeya problems on two extreme types of three dimensional Riemannian manifolds: Manifolds with the most symmetries (manifolds of constant sectional curvature) and manifolds with the...

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Classical Analysis and ODEs Papers @ClassicalODEs

Jun 12

An Oskolkov–Zhizhiashvili Criterion for Rectangular Fourier Sums Ushangi Goginava arxiv.org/abs/2606.12920 [𝚖𝚊𝚝𝚑.𝙲𝙰 𝚖𝚊𝚝𝚑.𝙰𝙿]

An Oskolkov--Zhizhiashvili Criterion for Rectangular Fourier Sums

Let $S_{\mathbf n}f$ denote the symmetric rectangular partial sums of the trigonometric Fourier series of a function on the $d$-dimensional torus. We prove a summable endpoint criterion at the...

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Classical Analysis and ODEs Papers @ClassicalODEs

Jun 12

Remarks on the Ionescu-Wainger multiplier theorem Dariusz Kosz, Mariusz Mirek, Wojciech Słomian, Jianghao Zhang arxiv.org/abs/2606.12663 [𝚖𝚊𝚝𝚑.𝙲𝙰]

Remarks on the Ionescu-Wainger multiplier theorem

In this paper, we extend the recent Ionescu--Wainger multiplier theorem for the set of canonical fractions by Kosz, Mirek, Peluse, Wan, and Wright in several directions. First, we prove its...

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Classical Analysis and ODEs Papers @ClassicalODEs

Jun 11

The general Brannan coefficient conjecture II: Meijer-function approximations T. M. Dunster arxiv.org/abs/2606.11621 [𝚖𝚊𝚝𝚑.𝙲𝙰 𝚖𝚊𝚝𝚑.𝙲𝚅]

The general Brannan coefficient conjecture II: Meijer-function...

The coefficients $A_n(α,β,ω)$ in the Maclaurin expansion $(1 ωz)^α(1-z)^{-β}=\sum_{n=0}^{\infty} A_n(α,β,ω)z^n$ are considered for $|ω|=1$ and...

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Classical Analysis and ODEs Papers @ClassicalODEs

Jun 10

A Resurgent Analytic Framework for Indicial Umbral Calculus via Mellin-Barnes and Borel-Laplace Theories Roberto Ricci arxiv.org/abs/2606.11134 [𝚖𝚊𝚝𝚑.𝙲𝙰] 💬Submitted to MDPI Axioms

A Resurgent Analytic Framework for Indicial Umbral Calculus via...

Indicial umbral calculus offers an effective operational framework for manipulating transcendental functions, yet its analytic foundations have long remained only partially understood. In this...

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Classical Analysis and ODEs Papers @ClassicalODEs

Jun 9

The Distance for Functions in BMO to BLO Hua Huang, Long Huang, Ciqiang Zhuo arxiv.org/abs/2606.09206 [𝚖𝚊𝚝𝚑.𝙲𝙰]

The Distance for Functions in BMO to BLO

In this article, we give the distance for a function $f$ of bounded mean oscillation to the space BLO($\Rn$) of functions of bounded lower oscillation via the Muckenhoupt weight class $A_p$ as...

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Classical Analysis and ODEs Papers @ClassicalODEs

Jun 9

On the Constant and Extremal Function for Weighted Hardy Inequality in Lₚ Ivan Gadjev arxiv.org/abs/2606.09067 [𝚖𝚊𝚝𝚑.𝙲𝙰]

On the Constant and Extremal Function for Weighted Hardy...

We study the behaviour of the smallest possible constant $d(a,b, p,ε)$ in Hardy inequality $$ \int_a^b\left(\frac{1}{x}\int_a^xf(t)dt\right)^px^ε\,dx\leq...

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Classical Analysis and ODEs Papers @ClassicalODEs

Jun 9

Weighted Hardy Inequality in l₂ Ivan Gadjev arxiv.org/abs/2606.09057 [𝚖𝚊𝚝𝚑.𝙲𝙰]

Weighted Hardy Inequality in $l_2$

We study the behaviour of the smallest possible constant $d_n$ in weighted Hardy inequality $$ \sum_{k=1}^{n}\Big(\frac{1}{k}\sum_{j=1}^{k}a_j\Big)^2 k^ε\le...

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Classical Analysis and ODEs Papers @ClassicalODEs

Jun 9

From generalized Poincaré to Poincaré-Sobolev inequalities via self-improving methods Alejandro Claros, Carlos Pérez, Linfei Zheng arxiv.org/abs/2606.08556 [𝚖𝚊𝚝𝚑.𝙲𝙰]

From generalized Poincaré to Poincaré-Sobolev inequalities via...

We establish several improvements to the main results of [PR19] and [CP21], refining the seminal self-improving method for generalized Poincaré inequalities from [FPW98, MP98]. These results,...

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Classical Analysis and ODEs Papers @ClassicalODEs

Jun 9

Functions of Bounded Variation and Point Processes J. Antezana, M. Levi, J. Marzo, J. Ortega-Cerdà arxiv.org/abs/2606.08304 [𝚖𝚊𝚝𝚑.𝙲𝙰 𝚖𝚊𝚝𝚑.𝙿𝚁]

Functions of Bounded Variation and Point Processes

We investigate the relationship between the analytical properties of functions of bounded variation and the statistical behavior of hyperuniform point processes. We establish several...

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Classical Analysis and ODEs Papers @ClassicalODEs

Jun 8

Discrete analogues in harmonic analysis: TT* methods Bartosz Langowski, Mariusz Mirek, Tomasz Z. Szarek arxiv.org/abs/2606.07359 [𝚖𝚊𝚝𝚑.𝙲𝙰]

Discrete analogues in harmonic analysis: $TT^*$ methods

In this note we present how the almost-orthogonality methods based on $TT^*$ arguments can be employed to study boundedness of discrete operators of Radon type. Almost-orthogonality methods have...

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Classical Analysis and ODEs Papers @ClassicalODEs

Jun 8

Fourier restriction estimates based on Lq-dimensions: beyond Stein–Tomas Marc Carnovale, Jonathan M. Fraser, Ana E. de Orellana arxiv.org/abs/2606.07143 [𝚖𝚊𝚝𝚑.𝙲𝙰 𝚖𝚊𝚝𝚑.𝙳𝚂 𝚖𝚊𝚝𝚑.𝙵𝙰 𝚖𝚊𝚝𝚑.𝙼𝙶 𝚖𝚊𝚝𝚑.𝙿𝚁]

Fourier restriction estimates based on $L^q$-dimensions: beyond...

The well-known Stein--Tomas restriction theorem gives the sharp range of $p$ for which $L^p\to L^2$ restriction estimates hold for the surface measure on the sphere. This was generalised to...

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