{"title":"Irreducibility of extensions of Laguerre polynomials","authors":"S. Laishram, Saranya G. Nair, T. Shorey","doi":"10.7169/facm/1748","DOIUrl":"https://doi.org/10.7169/facm/1748","url":null,"abstract":"For integers $a_0,a_1,ldots,a_n$ with $|a_0a_n|=1$ and either $alpha =u$ with $1leq u leq 50$ or $alpha=u+ frac{1}{2}$ with $1 leq u leq 45$, we prove that $psi_n^{(alpha)}(x;a_0,a_1,cdots,a_n)$ is irreducible except for an explicit finite set of pairs $(u,n)$. Furthermore all the exceptions other than $n=2^{12},alpha=89/2$ are necessary. The above result with $0leqalpha leq 10$ is due to Filaseta, Finch and Leidy and with $alpha in {-1/2,1/2}$ due to Schur.","PeriodicalId":44655,"journal":{"name":"FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2019-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48545905","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}
{"title":"Conical measures and closed vector measures","authors":"S. Okada, W. Ricker","doi":"10.7169/FACM/1711","DOIUrl":"https://doi.org/10.7169/FACM/1711","url":null,"abstract":"","PeriodicalId":44655,"journal":{"name":"FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2018-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41764774","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}
A. Defant, Domingo García, M. Maestre, P. Sevilla-Peris
{"title":"Dirichlet series from the infinite dimensional point of view","authors":"A. Defant, Domingo García, M. Maestre, P. Sevilla-Peris","doi":"10.7169/FACM/1741","DOIUrl":"https://doi.org/10.7169/FACM/1741","url":null,"abstract":"","PeriodicalId":44655,"journal":{"name":"FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2018-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.7169/FACM/1741","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46551474","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}
{"title":"On compactness of Toeplitz operators in Bergman spaces","authors":"J. Taskinen, J. Virtanen","doi":"10.7169/FACM/1727","DOIUrl":"https://doi.org/10.7169/FACM/1727","url":null,"abstract":"In this paper we consider Toepliz operators with (locally) integrable symbols acting on Bergman spaces Ap (1<p<∞) of the open unit disc of the complex plane. We give a characterization of compact Toeplitz operators with symbols in L1 under a mild additional condition. Our result is new even in the Hilbert space setting of A2, where it extends the well-known characterization of compact Toeplitz operators with bounded symbols by Stroethoff and Zheng.","PeriodicalId":44655,"journal":{"name":"FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2018-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.7169/FACM/1727","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45441393","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}
{"title":"WCG spaces and their subspaces grasped by projectional skeletons","authors":"M. Fabian, V. Montesinos","doi":"10.7169/FACM/1721","DOIUrl":"https://doi.org/10.7169/FACM/1721","url":null,"abstract":"Weakly compactly generated Banach spaces and their subspaces are characterized by the presence of projectional skeletons with some additional properties. We work with real spaces. However the presented statements can be extended, without much extra effort, to complex spaces.","PeriodicalId":44655,"journal":{"name":"FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2018-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.7169/FACM/1721","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44446676","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}
{"title":"Operators on Fock-type and weighted spaces of entire functions","authors":"Ó. Blasco","doi":"10.7169/FACM/1708","DOIUrl":"https://doi.org/10.7169/FACM/1708","url":null,"abstract":"","PeriodicalId":44655,"journal":{"name":"FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2018-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.7169/FACM/1708","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46143248","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}
{"title":"On the derivatives of the integer-valued polynomials","authors":"Bakir Farhi","doi":"10.7169/facm/1786","DOIUrl":"https://doi.org/10.7169/facm/1786","url":null,"abstract":"In this paper, we study the derivatives of an integer-valued polynomial of a given degree. Denoting by $E_n$ the set of the integer-valued polynomials with degree $leq n$, we show that the smallest positive integer $c_n$ satisfying the property: $forall P in E_n, c_n P' in E_n$ is $c_n = mathrm{lcm}(1 , 2 , dots , n)$. As an application, we deduce an easy proof of the well-known inequality $mathrm{lcm}(1 , 2 , dots , n) geq 2^{n - 1}$ ($forall n geq 1$). In the second part of the paper, we generalize our result for the derivative of a given order $k$ and then we give two divisibility properties for the obtained numbers $c_{n , k}$ (generalizing the $c_n$'s). Leaning on this study, we conclude the paper by determining, for a given natural number $n$, the smallest positive integer $lambda_n$ satisfying the property: $forall P in E_n$, $forall k in mathbb{N}$: $lambda_n P^{(k)} in E_n$. In particular, we show that: $lambda_n = prod_{p text{ prime}} p^{lfloorfrac{n}{p}rfloor}$ ($forall n in mathbb{N}$).","PeriodicalId":44655,"journal":{"name":"FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2018-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47332835","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}
{"title":"On an oscillatory integral involving a homogeneous form","authors":"S. Yamagishi","doi":"10.7169/facm/1775","DOIUrl":"https://doi.org/10.7169/facm/1775","url":null,"abstract":"Let $F in mathbb{R}[x_1, ldots, x_n]$ be a homogeneous form of degree $d > 1$ satisfying $(n - dim V_{F}^*) > 4$, where $V_F^*$ is the singular locus of $V(F) = { mathbf{z} in {mathbb{C}}^n: F(mathbf{z}) = 0 }$. Suppose there exists $mathbf{x}_0 in (0,1)^n cap (V(F) backslash V_F^*)$. Let $mathbf{t} = (t_1, ldots, t_n) in mathbb{R}^n$. Then for a smooth function $varpi:mathbb{R}^n rightarrow mathbb{R}$ with its support contained in a small neighbourhood of $mathbf{x}_0$, we prove $$ Big{|} int_{0}^{infty} cdots int_{0}^{infty} varpi(mathbf{x}) x_1^{i t_1} cdots x_n^{i t_n} e^{2 pi i tau F(mathbf{x})} d mathbf{x} Big{|} ll min { 1, |tau|^{-1} }, $$ where the implicit constant is independent of $tau$ and $mathbf{t}$.","PeriodicalId":44655,"journal":{"name":"FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2018-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41257188","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}
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