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A Note on the Mapping Theorem for Essential Pseudospectra in a Banach Space 关于巴拿赫空间本质伪谱映射定理的说明
IF 0.5 4区 数学
Ukrainian Mathematical Journal Pub Date : 2024-09-06 DOI: 10.1007/s11253-024-02326-7
Aymen Ammar, S. Veeramani
{"title":"A Note on the Mapping Theorem for Essential Pseudospectra in a Banach Space","authors":"Aymen Ammar, S. Veeramani","doi":"10.1007/s11253-024-02326-7","DOIUrl":"https://doi.org/10.1007/s11253-024-02326-7","url":null,"abstract":"<p>The main aim of the paper is to determine some basic properties of the essential pseudospectrum of a bounded linear operator <i>A</i> defined in a Banach space <i>X.</i> We also prove two different versions of the essential pseudospectral mapping theorem.</p>","PeriodicalId":49406,"journal":{"name":"Ukrainian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142226663","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
Laguerre–Cayley Functions and Related Polynomials 拉盖尔-凯利函数和相关多项式
IF 0.5 4区 数学
Ukrainian Mathematical Journal Pub Date : 2024-09-06 DOI: 10.1007/s11253-024-02332-9
Volodymyr Makarov, Serhii Makarov
{"title":"Laguerre–Cayley Functions and Related Polynomials","authors":"Volodymyr Makarov, Serhii Makarov","doi":"10.1007/s11253-024-02332-9","DOIUrl":"https://doi.org/10.1007/s11253-024-02332-9","url":null,"abstract":"<p>We study the main properties of the Laguerre–Cayley functions and related polynomials, which can be regarded as an essential component of the mathematical apparatus of the functional-discrete (FD-) method used to solve the Cauchy problem for an abstract homogeneous evolutionary equation of fractional order.</p>","PeriodicalId":49406,"journal":{"name":"Ukrainian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142211187","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
Sufficient Conditions and Radius Problems for the Silverman Class 西尔弗曼类的充分条件和半径问题
IF 0.5 4区 数学
Ukrainian Mathematical Journal Pub Date : 2024-09-06 DOI: 10.1007/s11253-024-02331-w
S. Sivaprasad Kumar, Priyanka Goel
{"title":"Sufficient Conditions and Radius Problems for the Silverman Class","authors":"S. Sivaprasad Kumar, Priyanka Goel","doi":"10.1007/s11253-024-02331-w","DOIUrl":"https://doi.org/10.1007/s11253-024-02331-w","url":null,"abstract":"<p>For 0 <i>&lt;</i> α ≤ 1 and <i>λ &gt;</i> 0<i>,</i> let</p><p><span>({G}_{lambda ,alpha }=left{f in A: left|frac{1-alpha +alpha zf^{primeprime}left(zright)/{f}^{{^{prime}}}left(zright)}{z{f}^{{^{prime}}}left(zright)/fleft(zright)}-left(1-alpha right)right|&lt; lambda , z in {mathbb{D}}right}. (0.1))</span></p><p>The general form of the Silverman class was introduced by Tuneski and Irmak [<i>Int. J. Math. Math. Sci.</i>, 2006, Article ID 38089 (2006)]. Our differential-inequality formulation is based on several sufficient conditions for this class. Further, we consider a class Ω given by</p><p><span>(Omega =left{fin A:left|z{f{^{prime}}}^{left(zright)}-fleft(zright)right|&lt;frac{1}{2},zin {mathbb{D}}right}. (0.2))</span></p><p>For these two classes, we establish inclusion relations involving some well-known subclasses of <i>S</i><sup><i>*</i></sup> and compute radius estimates featuring various pairings of these classes.</p>","PeriodicalId":49406,"journal":{"name":"Ukrainian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142211182","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
Leonardo and Hyper-Leonardo Numbers Via Riordan Arrays 通过瑞尔丹数组计算莱昂纳多和超莱昂纳多数
IF 0.5 4区 数学
Ukrainian Mathematical Journal Pub Date : 2024-09-06 DOI: 10.1007/s11253-024-02325-8
Yasemin Alp, E. Gokcen Kocer
{"title":"Leonardo and Hyper-Leonardo Numbers Via Riordan Arrays","authors":"Yasemin Alp, E. Gokcen Kocer","doi":"10.1007/s11253-024-02325-8","DOIUrl":"https://doi.org/10.1007/s11253-024-02325-8","url":null,"abstract":"<p>A generalization of the Leonardo numbers is defined and called hyper-Leonardo numbers. Infinite lowertriangular matrices whose elements are Leonardo and hyper-Leonardo numbers are considered. Then the <i>A</i>- and <i>Z</i>-sequences of these matrices are obtained. Finally, the combinatorial identities between the hyper-Leonardo and Fibonacci numbers are deduced by using the fundamental theorem on Riordan arrays.</p>","PeriodicalId":49406,"journal":{"name":"Ukrainian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142211186","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 Continuous Extension of the Cauchy-Type Integral with Parameter-Dependent Density to the Boundary of the Domain 论与参数相关密度的柯西式积分向域边界的连续扩展
IF 0.5 4区 数学
Ukrainian Mathematical Journal Pub Date : 2024-09-06 DOI: 10.1007/s11253-024-02335-6
Sergiy Plaksa
{"title":"On Continuous Extension of the Cauchy-Type Integral with Parameter-Dependent Density to the Boundary of the Domain","authors":"Sergiy Plaksa","doi":"10.1007/s11253-024-02335-6","DOIUrl":"https://doi.org/10.1007/s11253-024-02335-6","url":null,"abstract":"<p>We establish sufficient conditions for the continuous extension of a Cauchy-type integral whose density depends on the parameter to a nonsmooth integration line.</p>","PeriodicalId":49406,"journal":{"name":"Ukrainian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142227919","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
Relationship Between the Bojanov–Naidenov Problem and the Kolmogorov-Type Inequalities 波雅诺夫-奈德诺夫问题与科尔莫戈罗夫式不等式之间的关系
IF 0.5 4区 数学
Ukrainian Mathematical Journal Pub Date : 2024-09-06 DOI: 10.1007/s11253-024-02330-x
Volodymyr Kofanov
{"title":"Relationship Between the Bojanov–Naidenov Problem and the Kolmogorov-Type Inequalities","authors":"Volodymyr Kofanov","doi":"10.1007/s11253-024-02330-x","DOIUrl":"https://doi.org/10.1007/s11253-024-02330-x","url":null,"abstract":"<p>It is shown that the Bojanov–Naidenov problem <span>({Vert {x}^{left(kright)}Vert }_{q, delta })</span> → sup<i>, k</i> = 0<i>,</i> 1<i>, . . . , r −</i> 1<i>,</i> on the classes of functions <span>({Omega }_{p}^{r}left({A}_{0}, {A}_{r}right))</span> := <span>(left{x in {L}_{infty }^{r}: {Vert {x}^{left(rright)}Vert }_{infty }le {A}_{r}, L{left(xright)}_{p}le {A}_{0}right},)</span> where <i>q ≥</i> 1 for <i>k ≥</i> 1 and <i>q ≥ p</i> for <i>k</i> = 0<i>,</i> is equivalent to the problem of finding the sharp constant <i>C</i> = <i>C</i>(<i>λ</i>) in the Kolmogorov-type inequality</p><p><span>({Vert {x}^{left(rright)}Vert }_{q,delta }le CL{left(xright)}_{p}^{alpha }{Vert {x}^{left(rright)}Vert }_{infty }^{1-alpha }, xin {Omega }_{p,lambda }^{r}, (1))</span></p><p>where <span>(alpha =frac{r-k+1/q}{r+1/p},)</span> <span>({Vert xVert }_{p,delta })</span> := sup {<span>({Vert xVert }_{{L}_{p}[a,b]})</span>:a, b, ∈ <b>R</b>, 0 &lt; b – a ≤ δ} δ &gt; 0, <span>({Omega }_{p,lambda }^{r})</span> := <span>(bigcup left{{Omega }_{p}^{r}left({A}_{0}, {A}_{r}right):{A}_{0}={A}_{r}Lleft(varphi lambda ,rright)pright},)</span> ⋋ &gt; 0, φ⋋,r is a contraction of the ideal Euler spline of order r, and L<sub>(x)p</sub> : = sup {<span>({Vert xVert }_{{L}_{p}[a,b]}:)</span> a, b, ∈ <b>R</b> |x(t)| &gt; 0, t ∈ (a,b)}. In particular, we obtain a sharp inequality of the form (1) in the classes <span>({Omega }_{p,lambda }^{r},)</span> ⋋ &gt; 0. We also prove the theorems on relationships for the Bojanov–Naidenov problems in the spaces of trigonometric polynomials and splines and establish the corresponding sharp Bernstein-type inequalities.</p>","PeriodicalId":49406,"journal":{"name":"Ukrainian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142211184","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
Boundary-Value Problems for the Lyapunov Equation. I Lyapunov 方程的边值问题I
IF 0.5 4区 数学
Ukrainian Mathematical Journal Pub Date : 2024-09-06 DOI: 10.1007/s11253-024-02327-6
Oleksandr Boichuk, Evhen Panasenko, Oleksandr Pokutnyi
{"title":"Boundary-Value Problems for the Lyapunov Equation. I","authors":"Oleksandr Boichuk, Evhen Panasenko, Oleksandr Pokutnyi","doi":"10.1007/s11253-024-02327-6","DOIUrl":"https://doi.org/10.1007/s11253-024-02327-6","url":null,"abstract":"<p>We study boundary-value problems for the Lyapunov operator-differential equation. By using the theory of Moore–Penrose pseudoinverse operators and its generalizations, we establish conditions for the existence of generalized solutions and propose algorithms for their construction.</p>","PeriodicalId":49406,"journal":{"name":"Ukrainian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142211181","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
Fixed-Point Theorem for an Infinite Toeplitz Matrix and Its Extension to General Infinite Matrices 无穷托普利兹矩阵的定点定理及其对一般无穷矩阵的扩展
IF 0.5 4区 数学
Ukrainian Mathematical Journal Pub Date : 2024-09-06 DOI: 10.1007/s11253-024-02324-9
Vyacheslav M. Abramov
{"title":"Fixed-Point Theorem for an Infinite Toeplitz Matrix and Its Extension to General Infinite Matrices","authors":"Vyacheslav M. Abramov","doi":"10.1007/s11253-024-02324-9","DOIUrl":"https://doi.org/10.1007/s11253-024-02324-9","url":null,"abstract":"<p>In [V. M. Abramov, <i>Bull. Austral. Math. Soc.</i>, <b>104</b>, 108 (2021)], the fixed-point equation was studied for an infinite nonnegative particular Toeplitz matrix. In the present work, we provide an alternative proof of the existence of a positive solution in the general case. This proof is based on the application of a version of the M. A. Krasnosel’skii fixed-point theorem. The results are then extended to the equations with infinite matrices of the general type.</p>","PeriodicalId":49406,"journal":{"name":"Ukrainian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142211188","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
Rotational Interval Exchange Transformations 旋转间隔交换变换
IF 0.5 4区 数学
Ukrainian Mathematical Journal Pub Date : 2024-09-06 DOI: 10.1007/s11253-024-02334-7
Alexey Teplinsky
{"title":"Rotational Interval Exchange Transformations","authors":"Alexey Teplinsky","doi":"10.1007/s11253-024-02334-7","DOIUrl":"https://doi.org/10.1007/s11253-024-02334-7","url":null,"abstract":"<p>We prove the equivalence of two possible definitions of rotational interval exchange transformations: by the first definition, this is the first return map for the rotation of a circle onto a union of finitely many circle arcs, whereas by the second definition, this is an interval exchange with a scheme (in a sense of interval rearrangement ensemble) whose dual is also an interval exchange scheme.</p>","PeriodicalId":49406,"journal":{"name":"Ukrainian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142227918","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
Abelian Model Structures on Comma Categories 逗号范畴上的阿贝尔模型结构
IF 0.5 4区 数学
Ukrainian Mathematical Journal Pub Date : 2024-09-06 DOI: 10.1007/s11253-024-02328-5
Guoliang Tang
{"title":"Abelian Model Structures on Comma Categories","authors":"Guoliang Tang","doi":"10.1007/s11253-024-02328-5","DOIUrl":"https://doi.org/10.1007/s11253-024-02328-5","url":null,"abstract":"<p>Let A and B be bicomplete Abelian categories, which both have enough projectives and injectives and let <i>T</i> : A → B be a right exact functor. Under certain mild conditions, we show that hereditary Abelian model structures on A and B can be amalgamated into a global hereditary Abelian model structure on the comma category (<i>T</i> ↓ B)<i>.</i> As an application of this result, we give an explicit description of a subcategory that consists of all trivial objects of the Gorenstein flat model structure on the category of modules over a triangular matrix ring.</p>","PeriodicalId":49406,"journal":{"name":"Ukrainian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142211185","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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