Potential Analysis最新文献_第6页

Some Inequalities Between Ahlfors Regular Conformal Dimension And Spectral Dimensions For Resistance Forms 阻力形式的Ahlfors正则保形维数与谱维数之间的若干不等式

3区数学

Potential Analysis Pub Date : 2023-11-11 DOI: 10.1007/s11118-023-10112-6

Kôhei Sasaya

引用次数: 0

On the Restriction of a Right Process Outside a Negligible Set 可忽略集外右进程的约束

3区数学

Potential Analysis Pub Date : 2023-11-09 DOI: 10.1007/s11118-023-10114-4

Liping Li, Michael Röckner

引用次数: 0

Rank 5 Trivializable Subriemannian Structure on $$mathbb {S}^7$$ and Subelliptic Heat Kernel $$mathbb {S}^7$$和亚椭圆热核上的5阶可琐屑的subriemann结构

3区数学

Potential Analysis Pub Date : 2023-10-28 DOI: 10.1007/s11118-023-10110-8

Wolfram Bauer, Abdellah Laaroussi, Daisuke Tarama

{"title":"Rank 5 Trivializable Subriemannian Structure on $$mathbb {S}^7$$ and Subelliptic Heat Kernel","authors":"Wolfram Bauer, Abdellah Laaroussi, Daisuke Tarama","doi":"10.1007/s11118-023-10110-8","DOIUrl":"https://doi.org/10.1007/s11118-023-10110-8","url":null,"abstract":"Abstract We present an explicit form of the subelliptic heat kernel of the intrinsic sublaplacian $$Delta _{textrm{sub}}^5$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msubsup> <mml:mi>Δ</mml:mi> <mml:mrow> <mml:mtext>sub</mml:mtext> </mml:mrow> <mml:mn>5</mml:mn> </mml:msubsup> </mml:math> induced by a rank 5 trivializable subriemannian structure on the Euclidean seven dimensional sphere $$mathbb {S}^7$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msup> <mml:mrow> <mml:mi>S</mml:mi> </mml:mrow> <mml:mn>7</mml:mn> </mml:msup> </mml:math> . This completes the heat kernel analysis of trivializable subriemannian structures on $$mathbb {S}^7$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msup> <mml:mrow> <mml:mi>S</mml:mi> </mml:mrow> <mml:mn>7</mml:mn> </mml:msup> </mml:math> induced by a Clifford module action on $$mathbb {R}^8$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msup> <mml:mrow> <mml:mi>R</mml:mi> </mml:mrow> <mml:mn>8</mml:mn> </mml:msup> </mml:math> . As an application we derive the spectrum of $$Delta _{textrm{sub}}^5$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msubsup> <mml:mi>Δ</mml:mi> <mml:mrow> <mml:mtext>sub</mml:mtext> </mml:mrow> <mml:mn>5</mml:mn> </mml:msubsup> </mml:math> and the Green function of the conformal sublaplacian in an explicit form.","PeriodicalId":49679,"journal":{"name":"Potential Analysis","volume":"1 ","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136233562","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Extensions of Harmonic Functions of the Complex Plane Slit Along a Line Segment 复平面狭缝调和函数沿线段的扩展

3区数学

Potential Analysis Pub Date : 2023-10-19 DOI: 10.1007/s11118-023-10103-7

Armen Grigoryan, Andrzej Michalski, Dariusz Partyka

{"title":"Extensions of Harmonic Functions of the Complex Plane Slit Along a Line Segment","authors":"Armen Grigoryan, Andrzej Michalski, Dariusz Partyka","doi":"10.1007/s11118-023-10103-7","DOIUrl":"https://doi.org/10.1007/s11118-023-10103-7","url":null,"abstract":"Abstract Let I be a line segment in the complex plane $$mathbb C$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>C</mml:mi> </mml:math> . We describe a method of constructing a bi-Lipschitz sense-preserving mapping of $$mathbb C$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>C</mml:mi> </mml:math> onto itself, which is harmonic in $$mathbb Csetminus I$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>C</mml:mi> <mml:mo></mml:mo> <mml:mi>I</mml:mi> </mml:mrow> </mml:math> and coincides with a given sufficiently regular function $$f:Irightarrow mathbb C$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>f</mml:mi> <mml:mo>:</mml:mo> <mml:mi>I</mml:mi> <mml:mo>→</mml:mo> <mml:mi>C</mml:mi> </mml:mrow> </mml:math> . As a result we show that a quasiconformal self-mapping of $$mathbb C$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>C</mml:mi> </mml:math> which is harmonic in $$mathbb Csetminus I$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>C</mml:mi> <mml:mo></mml:mo> <mml:mi>I</mml:mi> </mml:mrow> </mml:math> does not have to be harmonic in $$mathbb C$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>C</mml:mi> </mml:math> .","PeriodicalId":49679,"journal":{"name":"Potential Analysis","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135730415","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Lower Bound for the Green Energy of Point Configurations in Harmonic Manifolds 调和流形中点构型绿色能量的下界

3区数学

Potential Analysis Pub Date : 2023-10-19 DOI: 10.1007/s11118-023-10108-2

Carlos Beltrán, Víctor de la Torre, Fátima Lizarte

引用次数: 0

A Convergence Rate for Extended-Source Internal DLA in the Plane 平面内扩展源DLA的收敛速率研究

3区数学

Potential Analysis Pub Date : 2023-10-16 DOI: 10.1007/s11118-023-10102-8

David Darrow

{"title":"A Convergence Rate for Extended-Source Internal DLA in the Plane","authors":"David Darrow","doi":"10.1007/s11118-023-10102-8","DOIUrl":"https://doi.org/10.1007/s11118-023-10102-8","url":null,"abstract":"Abstract Internal DLA (IDLA) is an internal aggregation model in which particles perform random walks from the origin, in turn, and stop upon reaching an unoccupied site. Levine and Peres showed that, when particles start instead from fixed multiple-point distributions, the modified IDLA processes have deterministic scaling limits related to a certain obstacle problem. In this paper, we investigate the convergence rate of this “extended source” IDLA in the plane to its scaling limit. We show that, if $$delta $$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>δ</mml:mi> </mml:math> is the lattice size, fluctuations of the IDLA occupied set are at most of order $$delta ^{3/5}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msup> <mml:mi>δ</mml:mi> <mml:mrow> <mml:mn>3</mml:mn> <mml:mo>/</mml:mo> <mml:mn>5</mml:mn> </mml:mrow> </mml:msup> </mml:math> from its scaling limit, with probability at least $$1-e^{-1/delta ^{2/5}}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>-</mml:mo> <mml:msup> <mml:mi>e</mml:mi> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>1</mml:mn> <mml:mo>/</mml:mo> <mml:msup> <mml:mi>δ</mml:mi> <mml:mrow> <mml:mn>2</mml:mn> <mml:mo>/</mml:mo> <mml:mn>5</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> .","PeriodicalId":49679,"journal":{"name":"Potential Analysis","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136077706","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 2

The Stochastic Klausmeier System and A Stochastic Schauder-Tychonoff Type Theorem 随机Klausmeier系统和一个随机Schauder-Tychonoff型定理

3区数学

Potential Analysis Pub Date : 2023-10-13 DOI: 10.1007/s11118-023-10107-3

Hausenblas, Erika, Tölle, Jonas M.

引用次数: 5

Harmonic Bergman Projectors on Homogeneous Trees 齐次树上的谐波Bergman投影

3区数学

Potential Analysis Pub Date : 2023-10-13 DOI: 10.1007/s11118-023-10106-4

Filippo De Mari, Matteo Monti, Maria Vallarino

{"title":"Harmonic Bergman Projectors on Homogeneous Trees","authors":"Filippo De Mari, Matteo Monti, Maria Vallarino","doi":"10.1007/s11118-023-10106-4","DOIUrl":"https://doi.org/10.1007/s11118-023-10106-4","url":null,"abstract":"Abstract In this paper we investigate some properties of the harmonic Bergman spaces $$mathcal A^p(sigma )$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:msup> <mml:mi>A</mml:mi> <mml:mi>p</mml:mi> </mml:msup> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>σ</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> on a q -homogeneous tree, where $$qge 2$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>q</mml:mi> <mml:mo>≥</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> , $$1le p<infty $$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>≤</mml:mo> <mml:mi>p</mml:mi> <mml:mo><</mml:mo> <mml:mi>∞</mml:mi> </mml:mrow> </mml:math> , and $$sigma $$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>σ</mml:mi> </mml:math> is a finite measure on the tree with radial decreasing density, hence nondoubling. These spaces were introduced by J. Cohen, F. Colonna, M. Picardello and D. Singman. When $$p=2$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>p</mml:mi> <mml:mo>=</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> they are reproducing kernel Hilbert spaces and we compute explicitely their reproducing kernel. We then study the boundedness properties of the Bergman projector on $$L^p(sigma )$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:msup> <mml:mi>L</mml:mi> <mml:mi>p</mml:mi> </mml:msup> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>σ</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> for $$1<p<infty $$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo><</mml:mo> <mml:mi>p</mml:mi> <mml:mo><</mml:mo> <mml:mi>∞</mml:mi> </mml:mrow> </mml:math> and their weak type (1,1) boundedness for radially exponentially decreasing measures on the tree. The weak type (1,1) boundedness is a consequence of the fact that the Bergman kernel satisfies an appropriate integral Hörmander’s condition.","PeriodicalId":49679,"journal":{"name":"Potential Analysis","volume":"255 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135858927","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 2

Dual Spaces for Weak Martingale Hardy Spaces Associated with Rearrangement-Invariant Spaces 与重排不变空间相关的弱鞅Hardy空间的对偶空间

3区数学

Potential Analysis Pub Date : 2023-10-11 DOI: 10.1007/s11118-023-10104-6

Xingyan Quan, Niyonkuru Silas, Guangheng Xie

引用次数: 0

Asymptotic Behavior for Multi-scale SDEs with Monotonicity Coefficients Driven by Lévy Processes lsamvy过程驱动的单调系数多尺度SDEs的渐近性

3区数学

Potential Analysis Pub Date : 2023-10-11 DOI: 10.1007/s11118-023-10105-5

Yinghui Shi, Xiaobin Sun, Liqiong Wang, Yingchao Xie

引用次数: 1