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Hardy inequalities and uncertainty principles in the presence of a black hole
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2024-12-18 DOI: 10.1007/s00013-024-02082-x
Miltiadis Paschalis
{"title":"Hardy inequalities and uncertainty principles in the presence of a black hole","authors":"Miltiadis Paschalis","doi":"10.1007/s00013-024-02082-x","DOIUrl":"10.1007/s00013-024-02082-x","url":null,"abstract":"<div><p>In this paper, we establish Hardy and Heisenberg uncertainty-type inequalities for the exterior of a Schwarzschild black hole. The weights that appear in both inequalities are tailored to fit the geometry, and can both be compared to the related Riemannian distance from the event horizon to yield inequalities for that distance. Moreover, in both cases the classic Euclidean inequalities with a point singularity can be recovered in the limit where one stands “far enough” from the black hole, as expected from the asymptotic flatness of the metric.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"124 2","pages":"205 - 218"},"PeriodicalIF":0.5,"publicationDate":"2024-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143108976","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Alternating state complexity of the set of primes and squarefree integers
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2024-12-17 DOI: 10.1007/s00013-024-02075-w
Jan-Christoph Schlage-Puchta
{"title":"Alternating state complexity of the set of primes and squarefree integers","authors":"Jan-Christoph Schlage-Puchta","doi":"10.1007/s00013-024-02075-w","DOIUrl":"10.1007/s00013-024-02075-w","url":null,"abstract":"<div><p>We show that the set of prime numbers has exponential alternating complexity, proving a conjecture by Fijalkow. We further show that the set of squarefree integers has essentially maximal possible alternating complexity.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"124 2","pages":"151 - 156"},"PeriodicalIF":0.5,"publicationDate":"2024-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00013-024-02075-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143108804","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Sharp bounds for the norm of the traceless second fundamental form of complete linear Weingarten spacelike hypersurfaces
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2024-12-01 DOI: 10.1007/s00013-024-02073-y
Jogli G. Araújo, Eudes L. de Lima, Henrique F. de Lima
{"title":"Sharp bounds for the norm of the traceless second fundamental form of complete linear Weingarten spacelike hypersurfaces","authors":"Jogli G. Araújo,&nbsp;Eudes L. de Lima,&nbsp;Henrique F. de Lima","doi":"10.1007/s00013-024-02073-y","DOIUrl":"10.1007/s00013-024-02073-y","url":null,"abstract":"<div><p>We establish sharp bounds for the norm of the traceless second fundamental form of complete linear Weingarten spacelike hypersurfaces immersed in a Lorentzian space form and satisfying a suitable Okumura type inequality. As a consequence of these estimates, we derive new characterization results concerning totally umbilical spacelike hypersurfaces and hyperbolic cylinders of Lorentzian space forms.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"124 2","pages":"219 - 231"},"PeriodicalIF":0.5,"publicationDate":"2024-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143108185","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
On Dirac equations with Hartree type nonlinearity in modulation spaces
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2024-11-28 DOI: 10.1007/s00013-024-02079-6
Seongyeon Kim, Hyeongjin Lee, Ihyeok Seo
{"title":"On Dirac equations with Hartree type nonlinearity in modulation spaces","authors":"Seongyeon Kim,&nbsp;Hyeongjin Lee,&nbsp;Ihyeok Seo","doi":"10.1007/s00013-024-02079-6","DOIUrl":"10.1007/s00013-024-02079-6","url":null,"abstract":"<div><p>We obtain the local well-posedness for Dirac equations with a Hartree type nonlinearity derived by decoupling the Dirac–Klein–Gordon system. We extend the function space of initial data, enabling us to handle initial data that were not addressed in previous studies.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"124 2","pages":"195 - 204"},"PeriodicalIF":0.5,"publicationDate":"2024-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143110082","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Linear topological invariants for kernels of differential operators by shifted fundamental solutions
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2024-11-24 DOI: 10.1007/s00013-024-02070-1
Andreas Debrouwere, Thomas Kalmes
{"title":"Linear topological invariants for kernels of differential operators by shifted fundamental solutions","authors":"Andreas Debrouwere,&nbsp;Thomas Kalmes","doi":"10.1007/s00013-024-02070-1","DOIUrl":"10.1007/s00013-024-02070-1","url":null,"abstract":"<div><p>We characterize the condition <span>((Omega ))</span> for smooth kernels of partial differential operators in terms of the existence of shifted fundamental solutions satisfying certain properties. The conditions <span>((POmega ))</span> and <span>((Poverline{overline{Omega }}))</span> for distributional kernels are characterized in a similar way. By lifting theorems for Fréchet spaces and (PLS)-spaces, this provides characterizations of the problem of parameter dependence for smooth and distributional solutions of differential equations by shifted fundamental solutions. As an application, we give a new proof of the fact that the space <span>({ f in {mathscr {E}}(X) , | , P(D)f = 0})</span> satisfies <span>((Omega ))</span> for any differential operator <i>P</i>(<i>D</i>) and any open convex set <span>(X subseteq {mathbb {R}}^d)</span>.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"124 2","pages":"177 - 193"},"PeriodicalIF":0.5,"publicationDate":"2024-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00013-024-02070-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143109116","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Rotators-translators to mean curvature flow in (mathbb {H}^2times mathbb {R}) 在 （ （mathbb {H}^2times （mathbb {R} ）中的平均曲率流的旋转器-平移器
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2024-11-21 DOI: 10.1007/s00013-024-02076-9
R. F. de Lima, A. K. Ramos, J. P. dos Santos
{"title":"Rotators-translators to mean curvature flow in (mathbb {H}^2times mathbb {R})","authors":"R. F. de Lima,&nbsp;A. K. Ramos,&nbsp;J. P. dos Santos","doi":"10.1007/s00013-024-02076-9","DOIUrl":"10.1007/s00013-024-02076-9","url":null,"abstract":"<div><p>We establish the existence of one-parameter families of helicoidal surfaces of <span>(mathbb H^2times mathbb R)</span> which, under mean curvature flow, simultaneously rotate about a vertical axis and translate vertically.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"124 3","pages":"343 - 353"},"PeriodicalIF":0.5,"publicationDate":"2024-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143184868","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
A remark on the Brill–Noether theory of curves of fixed gonality 关于固定向性曲线的Brill-Noether理论的评述
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2024-11-19 DOI: 10.1007/s00013-024-02059-w
Gerriet Martens
{"title":"A remark on the Brill–Noether theory of curves of fixed gonality","authors":"Gerriet Martens","doi":"10.1007/s00013-024-02059-w","DOIUrl":"10.1007/s00013-024-02059-w","url":null,"abstract":"<div><p>Recently the Brill–Noether theory of curves <i>C</i> of both fixed genus and gonality was established. In particular, in this theory (now called the Hurwitz–Brill–Noether theory), all irreducible components of the variety of complete linear series of a fixed degree and dimension on <i>C</i> are obtained from the closures of certain so-called “Brill–Noether splitting loci” (loci which have a rather succinct description). In this paper, a method previously invented for the construction of some of these irreducible components is applied to get simply designed varieties inside the difference between these splitting loci and their closures, i.e., inside the boundary of the splitting loci.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"124 1","pages":"49 - 61"},"PeriodicalIF":0.5,"publicationDate":"2024-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00013-024-02059-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142963144","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the transitivity of Lie ideals and a characterization of perfect Lie algebras 李理想的及及性及完备李代数的一个刻划
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2024-11-18 DOI: 10.1007/s00013-024-02063-0
Nikolaos Panagiotis Souris
{"title":"On the transitivity of Lie ideals and a characterization of perfect Lie algebras","authors":"Nikolaos Panagiotis Souris","doi":"10.1007/s00013-024-02063-0","DOIUrl":"10.1007/s00013-024-02063-0","url":null,"abstract":"<div><p>We explore general intrinsic and extrinsic conditions that allow the transitivity of the relation of being an ideal in Lie algebras. We also prove that perfect Lie algebras of arbitrary dimension and over any field are intrinsically characterized by transitivity of this type. In particular, we show that a Lie algebra <span>(mathfrak {h})</span> is perfect (i.e., <span>(mathfrak {h}=[mathfrak {h}, mathfrak {h}])</span>) if and only if for all Lie algebras <span>(mathfrak {k}, mathfrak {g})</span> such that <span>(mathfrak {h})</span> is an ideal of <span>(mathfrak {k})</span> and <span>(mathfrak {k})</span> is an ideal of <span>(mathfrak {g})</span>, it follows that <span>(mathfrak {h})</span> is an ideal of <span>(mathfrak {g})</span>.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"124 1","pages":"9 - 18"},"PeriodicalIF":0.5,"publicationDate":"2024-11-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142963143","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
On effective multiplicity one for modular forms of half-integral weight 半积分权的模形式的有效重数1
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2024-11-18 DOI: 10.1007/s00013-024-02057-y
Ratnadeep Acharya, Manish Kumar Pandey
{"title":"On effective multiplicity one for modular forms of half-integral weight","authors":"Ratnadeep Acharya,&nbsp;Manish Kumar Pandey","doi":"10.1007/s00013-024-02057-y","DOIUrl":"10.1007/s00013-024-02057-y","url":null,"abstract":"<div><p>In this article, we have considered the problem of effective determination of modular forms of half-integral weight in the weight aspect. The result is a generalization of a result of Munshi to the case of modular forms of half-integral weight.\u0000</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"124 1","pages":"19 - 27"},"PeriodicalIF":0.5,"publicationDate":"2024-11-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142963142","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Asymptotic behaviors of normalized ground states for fractional Schrödinger equations 分数阶Schrödinger方程归一化基态的渐近行为
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2024-11-16 DOI: 10.1007/s00013-024-02069-8
Jun Lei, Chunliu Chen, Yue Wang
{"title":"Asymptotic behaviors of normalized ground states for fractional Schrödinger equations","authors":"Jun Lei,&nbsp;Chunliu Chen,&nbsp;Yue Wang","doi":"10.1007/s00013-024-02069-8","DOIUrl":"10.1007/s00013-024-02069-8","url":null,"abstract":"<div><p>This article concerns a connection between the fractional Schrödinger equation and the logarithmic fractional Schrödinger equation. By rescaling and the constrained minimization method, we prove the asymptotic behaviors of normalized ground states for two equations.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"124 1","pages":"109 - 120"},"PeriodicalIF":0.5,"publicationDate":"2024-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142963104","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
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