Bulletin of the
Korean Mathematical Society
BKMS
ISSN(Print) 1015-8634
ISSN(Online) 2234-3016
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2023-05-31
On the hybrid mean value of generalized Dedekind sums, generalized Hardy sums and Kloosterman sums
Qing Tian, Yan WangAbstract : The main purpose of this paper is to study the hybrid mean value problem involving generalized Dedekind sums, generalized Hardy sums and Kloosterman sums. Some exact computational formulas are given by using the properties of Gauss sums and the mean value theorem of the Dirichlet L-function. A result of W. Peng and T. P. Zhang [12] is extended. The new results avoid the restriction that $q$ is a prime.
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2023-11-30
Operators $A$, $B$ for which the Aluthge transform $\widetilde{AB}$ is a generalised $n$-projection
Bhagwati Duggal, In Hyoun KimAbstract : A Hilbert space operator $A\in{\mathcal B(H)}$ is a generalised \linebreak $n$-projection, denoted $A\in (G-n-P)$, if ${A^*}^n=A$. $(G-n-P)$-operators $A$ are normal operators with finitely countable spectra $\sigma(A)$, subsets of the set $\{0\}\cup\{\sqrt[n+1]{1}\}$. The Aluthge transform $\tilde{A}$ of $A\in{\mathcal B(H)}$ may be $(G-n-P)$ without $A$ being $(G-n-P)$. For doubly commuting operators $A, B\in{\mathcal B(H)}$ such that $\sigma(AB)=\sigma(A)\sigma(B)$ and $\|A\|\|B\|\leq \left\|\widetilde{AB}\right\|$, $\widetilde{AB}\in (G-n-P)$ if and only if $A=\left\|\tilde{A}\right\|(A_{00}\oplus(A_{0}\oplus A_u))$ and $B=\left\|\tilde{B}\right\|(B_0\oplus B_u)$, where $A_{00}$ and $B_0$, and $A_0\oplus A_u$ and $B_u$, doubly commute, $A_{00}B_0$ and $A_0$ are 2 nilpotent, $A_u$ and $B_u$ are unitaries, $A^{*n}_u=A_u$ and $B^{*n}_u=B_u$. Furthermore, a necessary and sufficient condition for the operators $\alpha A$, $\beta B$, $\alpha \tilde{A}$ and $\beta \tilde{B}$, $\alpha=\frac{1}{\left\|\tilde{A}\right\|}$ and $\beta=\frac{1}{\left\|\tilde{B}\right\|}$, to be $(G-n-P)$ is that $A$ and $B$ are spectrally normaloid at $0$.
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2023-09-30
Relationship between the structure of a factor ring $R/P$ and derivations of $R$
Karim Bouchannafa, Moulay Abdallah Idrissi, Lahcen OukhtiteAbstract : The purpose of this paper is to study the relationship between the structure of a factor ring $R/P$ and the behavior of some derivations of $R$. More precisely, we establish a connection between the commutativity of $R/P$ and derivations of $R$ satisfying specific identities involving the prime ideal $P$. Moreover, we provide an example to show that our results cannot be extended to semi-prime ideals.
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2023-11-30
Two-weight norm estimates for square functions associated to fractional Schr{\"o}dinger operators with Hardy potential
Tongxin Kang, Yang ZouAbstract : Let $d\in\mathbb{N}$ and ${\alpha}\in(0,\min\{2,d\})$. For any $a\in[a^\ast,\infty)$, the fractional Schr\"odinger operator $\mathcal{L}_a$ is defined by \begin{equation*} \mathcal{L}_a:=(-\Delta)^{{\alpha}/2}+a{|x|}^{-{\alpha}}, \end{equation*} where $a^*:=-{\frac{2^{\alpha}{\Gamma}((d+{\alpha})/4)^2}{{\Gamma}((d-{\alpha})/4)^2}}$. In this paper, we study two-weight Sobolev inequalities associated with $\mathcal{L}_a$ and two-weight norm estimates for several square functions associated with $\mathcal{L}_a$.
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2023-03-31
On nuclearity of semigroup crossed products
Qing MengAbstract : In this paper, we study nuclearity of semigroup crossed products for quasi-lattice ordered groups. We show the relationships among nuclearity of the semigroup crossed product, amenability of the quasi-lattice ordered group and nuclearity of the underlying $C^*$-algebra.
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2024-05-31
On weakly $(m,n)$-prime ideals of commutative rings
Hani A. Khashan, Ece Yetkin CelikelAbstract : Let $R$ be a commutative ring with identity and $m$, $n$ be positive integers. In this paper, we introduce the class of weakly $(m,n)$-prime ideals generalizing $(m,n)$-prime and weakly $(m,n)$-closed ideals. A proper ideal $I$ of $R$ is called weakly $(m,n)$-prime if for $a,b\in R$, $0\neq a^{m}b\in I$ implies either $a^{n}\in I$ or $b\in I$. We justify several properties and characterizations of weakly $(m,n)$-prime ideals with many supporting examples. Furthermore, we investigate weakly $(m,n)$-prime ideals under various contexts of constructions such as direct products, localizations and homomorphic images. Finally, we discuss the behaviour of this class of ideals in idealization and amalgamated rings.
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2024-01-31
An Abelian category of weakly cofinite modules
Gholamreza PirmohammadiAbstract : Let $I$ be an ideal of a commutative Noetherian semi-local ring $R$ and $M$ be an $R$-module. It is shown that if $\dim M\leq 2$ and $\Supp_R M\subseteq V(I)$, then $M$ is $I$-weakly cofinite if (and only if) the $R$-modules $\Hom_R(R/I,M)$ and $\Ext^1_R(R/I,M)$ are weakly Laskerian. As a consequence of this result, it is shown that the category of all $I$-weakly cofinite modules $X$ with $\dim X\leq 2$, forms an Abelian subcategory of the category of all $R$-modules. Finally, it is shown that if $\dim R/I\leq 2$, then for each pair of finitely generated $R$-modules $M$ and $N$ and each pair of the integers $i,j\geq 0$, the $R$-modules $\Tor_i^R(N,H^j_I(M))$ and $\Ext^i_R(N,H^j_I(M))$ are $I$-weakly cofinite.
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2023-05-31
Vanishing theorems for weighted harmonic $1$-forms on smooth metric measure spaces
Xiaoli Chao, Weili WangAbstract : In this paper, we prove some vanishing theorems under the assumptions of weighted BiRic curvature or $m$-Bakry-\'{E}mery-Ricci curvature bounded from below.
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2023-09-30
Conditional Fourier--Feynman transform and conditional convolution product associated with infinite dimensional conditioning function
Jae Gil Choi, Sang Kil ShimAbstract : In this paper, we use an infinite dimensional conditioning function to define a conditional Fourier--Feynman transform (CFFT) and a conditional convolution product (CCP) on the Wiener space. We establish the existences of the CFFT and the CCP for bounded functions which form a Banach algebra. We then provide fundamental relationships between the CFFTs and the CCPs.
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2023-11-30
Bredon homology of wallpaper groups
Ramon FloresAbstract : In this paper we compute the Bredon homology of wallpaper groups with respect to the family of finite groups and with coefficients in the complex representation ring. We provide explicit bases of the homology groups in terms of irreducible characters of the stabilizers.
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On certain estimates for rough generalized parametric Marcinkiewicz integrals
Daiqing Zhang
Bull. Korean Math. Soc. 2023; 60(1): 47-73
https://doi.org/10.4134/BKMS.b210850 -
Six dimensional almost complex torus manifolds with Euler number six
Donghoon Jang, Jiyun Park
Bull. Korean Math. Soc. 2024; 61(2): 557-584
https://doi.org/10.4134/BKMS.b230227 -
MacWilliams-type identities on vectorial Boolean functions with bent components and applications
Jong Yoon Hyun
Bull. Korean Math. Soc. 2023; 60(3): 561-574
https://doi.org/10.4134/BKMS.b210374 -
Certain properties of the class of univalent functions with real coefficients
Milutin Obradovic, Nikola Tuneski
Bull. Korean Math. Soc. 2023; 60(5): 1253-1263
https://doi.org/10.4134/BKMS.b220643
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Differences of weighted composition operators on Bergman spaces induced by doubling weights
Jiale Chen
Bull. Korean Math. Soc. 2023; 60(5): 1201-1219
https://doi.org/10.4134/BKMS.b220578 -
On delay differential equations with meromorphic solutions of hyper-order less than one
Risto Korhonen, Yan Liu
Bull. Korean Math. Soc. 2024; 61(1): 229-246
https://doi.org/10.4134/BKMS.b230089 -
An extension of Schneider's characterization theorem for ellipsoids
Dong-Soo Kim, Young Ho Kim
Bull. Korean Math. Soc. 2023; 60(4): 905-913
https://doi.org/10.4134/BKMS.b220393 -
Classification of twisted product lightlike submanifolds
Sangeet Kumar, Megha Pruthi
Bull. Korean Math. Soc. 2023; 60(4): 1003-1016
https://doi.org/10.4134/BKMS.b220452
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