Pub Date : 2023-12-31DOI: 10.1007/s40574-023-00403-6
H. Kalita, B. Hazarika
{"title":"Kluvánek–Lewis–Henstock integral in Banach spaces","authors":"H. Kalita, B. Hazarika","doi":"10.1007/s40574-023-00403-6","DOIUrl":"https://doi.org/10.1007/s40574-023-00403-6","url":null,"abstract":"","PeriodicalId":214688,"journal":{"name":"Bollettino dell'Unione Matematica Italiana","volume":"116 9","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139135158","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-20DOI: 10.1007/s40574-023-00404-5
M. Cantarini
{"title":"Correction to: On the interplay between hypergeometric series, Fourier–Legendre expansions and Euler sums","authors":"M. Cantarini","doi":"10.1007/s40574-023-00404-5","DOIUrl":"https://doi.org/10.1007/s40574-023-00404-5","url":null,"abstract":"","PeriodicalId":214688,"journal":{"name":"Bollettino dell'Unione Matematica Italiana","volume":"117 37","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138958440","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-09DOI: 10.1007/s40574-023-00401-8
R. Labbas, S. Maingot, A. Thorel
{"title":"Solvability of a fourth order elliptic problem in a bounded sector, part I","authors":"R. Labbas, S. Maingot, A. Thorel","doi":"10.1007/s40574-023-00401-8","DOIUrl":"https://doi.org/10.1007/s40574-023-00401-8","url":null,"abstract":"","PeriodicalId":214688,"journal":{"name":"Bollettino dell'Unione Matematica Italiana","volume":"4 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138585583","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-09DOI: 10.1007/s40574-023-00398-0
N. Chernyavskaya, L. Shuster
{"title":"Principal fundamental system of solutions, the Hartman-Wintner problem and correct solvability of the general Sturm-Liouville equation","authors":"N. Chernyavskaya, L. Shuster","doi":"10.1007/s40574-023-00398-0","DOIUrl":"https://doi.org/10.1007/s40574-023-00398-0","url":null,"abstract":"","PeriodicalId":214688,"journal":{"name":"Bollettino dell'Unione Matematica Italiana","volume":" 36","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135291032","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-02DOI: 10.1007/s40574-023-00390-8
Sabino Di Trani
Abstract We present some results about the irreducible representations appearing in the exterior algebra $$Lambda mathfrak {g}$$ Λg , where $$mathfrak {g}$$ g is a simple Lie algebra over $${mathbb {C}}$$ C . For Lie algebras of type B , C or D we prove that certain irreducible representations, associated to weights characterized in a combinatorial way, appear as irreducible components of $$Lambda mathfrak {g}$$ Λg . Moreover, we propose an analogue of a conjecture of Kostant, about irreducibles appearing in the exterior algebra of the little adjoint representation. Finally, we give some closed expressions, in type B , C and D , for generalized exponents of small representations that are fundamental representations and we propose a generalization of some results of De Concini, Möseneder Frajria, Procesi and Papi about the module of special covariants of adjoint and little adjoint type.
{"title":"On the spectrum of exterior algebra, and generalized exponents of small representations","authors":"Sabino Di Trani","doi":"10.1007/s40574-023-00390-8","DOIUrl":"https://doi.org/10.1007/s40574-023-00390-8","url":null,"abstract":"Abstract We present some results about the irreducible representations appearing in the exterior algebra $$Lambda mathfrak {g}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>Λ</mml:mi> <mml:mi>g</mml:mi> </mml:mrow> </mml:math> , where $$mathfrak {g}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>g</mml:mi> </mml:math> is a simple Lie algebra over $${mathbb {C}}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>C</mml:mi> </mml:math> . For Lie algebras of type B , C or D we prove that certain irreducible representations, associated to weights characterized in a combinatorial way, appear as irreducible components of $$Lambda mathfrak {g}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>Λ</mml:mi> <mml:mi>g</mml:mi> </mml:mrow> </mml:math> . Moreover, we propose an analogue of a conjecture of Kostant, about irreducibles appearing in the exterior algebra of the little adjoint representation. Finally, we give some closed expressions, in type B , C and D , for generalized exponents of small representations that are fundamental representations and we propose a generalization of some results of De Concini, Möseneder Frajria, Procesi and Papi about the module of special covariants of adjoint and little adjoint type.","PeriodicalId":214688,"journal":{"name":"Bollettino dell'Unione Matematica Italiana","volume":"23 8","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135876625","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-02DOI: 10.1007/s40574-023-00397-1
Sorin G. Gal, Constantin P. Niculescu
{"title":"Degree of convergence in operator versions of nonlinear Korovkin’s theorems","authors":"Sorin G. Gal, Constantin P. Niculescu","doi":"10.1007/s40574-023-00397-1","DOIUrl":"https://doi.org/10.1007/s40574-023-00397-1","url":null,"abstract":"","PeriodicalId":214688,"journal":{"name":"Bollettino dell'Unione Matematica Italiana","volume":"7 11","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135972715","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-31DOI: 10.1007/s40574-023-00394-4
Michael Bildhauer, Martin Fuchs
Abstract Splitting-type variational problems $$begin{aligned} int _{Omega }sum _{i=1}^n f_i(partial _i w) , textrm{d}xrightarrow min end{aligned}$$ ∫Ω∑i=1nfi(∂iw)dx→min with superlinear growth conditions are studied by assuming $$begin{aligned} h_i(t) le f''_i(t) le H_i(t) qquad (*) end{aligned}$$ hi(t)≤fi′′(t)≤Hi(t)(∗) with suitable functions $$h_i$$ hi , $$H_i$$ Hi : $$mathbb {R}rightarrow mathbb {R}^+$$ R→R+ , $$i=1$$ i=1 , ..., n , measuring the growth and ellipticity of the energy density. Here, as the main feature, we do not impose a symmetric behaviour like $$h_i(t)approx h_i(-t)$$ hi(t)≈hi(
摘要研究了具有超线性增长条件的分裂型变分问题$$begin{aligned} int _{Omega }sum _{i=1}^n f_i(partial _i w) , textrm{d}xrightarrow min end{aligned}$$∫Ω∑i = 1 n f i(∂i w) d x→min，假设$$begin{aligned} h_i(t) le f''_i(t) le H_i(t) qquad (*) end{aligned}$$ h i (t)≤f i ' ' (t)≤h i (t)(∗)，并具有合适的函数$$h_i$$ h i, $$H_i$$ h i: $$mathbb {R}rightarrow mathbb {R}^+$$ R→R +， $$i=1$$ i = 1，…， n，测量能量密度的增长和椭圆度。在这里，作为主要特征，我们没有强加像$$h_i(t)approx h_i(-t)$$ h i (t)≈h i (- t)和$$H_i(t) approx H_i(-t)$$ h i (t)≈h i (- t)对于大的| t |的对称行为。在对$$(*)$$(∗)中出现的函数进行相当弱的假设的情况下，我们利用一个具有负指数幂权的caccioppolii型不等式，建立了局部极小值$$uin L^infty (Omega )$$ u∈L∞(Ω)的$$|nabla u|$$ |∇u |高可积性。
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