Hokkaido Mathematical Journal

No. 2

VIRDOL, Cristian;

The critical values of $L$-functions of base change for Hilbert modular forms.

Hokkaido Mathematical Journal, 48 (2019) pp.245-252

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Abstract

In this paper we generalize some results, obtained by Shimura, Yoshida and the author, on critical values of $L$-functions of $l$-adic representations attached to Hilbert modular forms twisted by finite order characters, to the critical values of $L$-functions of arbitrary base change to totally real number fields of $l$-adic representations attached to Hilbert modular forms twisted by some general finite-dimensional representations.

MSC(Primary)	11F41
MSC(Secondary)	11F80; 11R42; 11R80;
Uncontrolled Keywords	$L$-functions; special values; Hilbert modular forms;

ABU-DAWWAS, Rashid; BATAINEH, Malik; DA'KEEK, Adeela;

Graded weak comultiplication modules.

Hokkaido Mathematical Journal, 48 (2019) pp.253-261

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Abstract

Let $G$ be a group with identity $e$, $R$ be a $G$-graded ring and $M$ be a $G$-graded $R$-module. In this article, we introduce the concept of graded weak comultiplication modules. A graded $R$-module $M$ is said to be graded weak comultiplication if for every graded prime $R$-submodule $N$ of $M$, $N=(0:_{M}I)$ for some graded ideal $I$ of $R$. We study graded weak comultiplication modules and give several results.

MSC(Primary)	13A02
MSC(Secondary)
Uncontrolled Keywords	graded weak comultiplication modules; graded multiplication modules; graded modules;

ITOH, Kentaro; SAKAI, Ryozi; SUZUKI, Noriaki;

Uniform convergence of orthogonal polynomial expansions for exponential weights.

Hokkaido Mathematical Journal, 48 (2019) pp.263-280

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Abstract

We consider an exponential weight $w(x) = \exp(-Q(x))$ on ${\mathbb R} = (-\infty,\infty)$, where $Q$ is an even and nonnegative function on ${\mathbb R}$. We always assume that $w$ belongs to a relevant class $\mathcal{F}(C^2+)$. Let $\{p_n\}$ be orthogonal polynomials for a weight $w$. For a function $f$ on ${\mathbb R}$, $s_n(f)$ denote the $(n-1)$-th partial sum of Fourier series. In this paper, we discuss uniformly convergence of $s_n(f)$ under the conditions that $f$ is continuous and has a bounded variation on any compact interval of ${\mathbb R}$. In the proof of main theorem, Nikolskii-type inequality and boundedness of the de la Vall{\'{e}}e Poussin mean of $f$ play important roles.

MSC(Primary)	41A17
MSC(Secondary)	41A10;
Uncontrolled Keywords	uniformly convergence of Fourier series; weighted polynomial approximation; Erdős type weight; de la Vallée Poussin mean; Nikolskii-type inequality;

PEMBER, Mason; ROSSMAN, Wayne; SAJI, Kentaro; TERAMOTO, Keisuke;

Characterizing singularities of a surface in Lie sphere geometry.

Hokkaido Mathematical Journal, 48 (2019) pp.281-308

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Abstract

The conditions for a cuspidal edge, swallowtail and other fundamental singularities are given in the context of Lie sphere geometry. We then use these conditions to study the Lie sphere transformations of a surface.

MSC(Primary)	53A05
MSC(Secondary)	53A35; 57R45;
Uncontrolled Keywords	singularities; Lie sphere transformation;

SHI, Jiangtao;

A finite group in which all non-nilpotent maximal subgroups are normal has a Sylow tower.

Hokkaido Mathematical Journal, 48 (2019) pp.309-312

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Abstract

In this paper we prove that a finite group in which all non-nilpotent maximal subgroups are normal must have a Sylow tower, which improves Theorem 1.3 of [Finite groups with non-nilpotent maximal subgroups, Monatsh Math. 171 (2013) 425–431.].

MSC(Primary)	20D10
MSC(Secondary)
Uncontrolled Keywords	non-nilpotent maximal subgroup; normal; solvable; Sylow tower;

YOSHIDA, Masaaki;

Hypergeometric functions interpolating Appell-Lauricella's $F_D$ and $F_A$.

Hokkaido Mathematical Journal, 48 (2019) pp.313-325

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Abstract

For Appell-Lauricella's $F_D$, solutions represented by integrals of Euler type over various chambers are studied to re-discover the multiple hypergeometric functions introduced in [Ex]. A family of hypergeometric functions interpolating $F_D$ and $F_A$ is presented.

MSC(Primary)	33C65
MSC(Secondary)
Uncontrolled Keywords	Appell-Lauricella's hypergeometric functions;

IIDA, Takeshi;

Note on the integral operators in weighted Morrey spaces.

Hokkaido Mathematical Journal, 48 (2019) pp.327-343

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Abstract

We investigate the boundedness of the maximal operator, the fractional maximal operator, and the fractional integral operator within the framework of weighted Morrey spaces. In particular, we consider the endpoint cases. This result can be recognized as the endpoint case of two weight multilinear norm inequality [4, Theorem 3.3] and, as a special case, recovers the Olsen inequality with small parameters [9, Examples 4.7].

MSC(Primary)	26A33
MSC(Secondary)	42B25;
Uncontrolled Keywords	fractional maximal operator; fractional integral operator; weight; Morrey space;

ODA, Fumihito; WAKATAKE, Masahiro;

The unit group of a partial Burnside ring of a reducible Coxeter group of type A.

Hokkaido Mathematical Journal, 48 (2019) pp.345-356

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Abstract

We determine the structure of the unit group of the partial Burnside ring relative to the set of parabolic subgroups of a finite reducible Coxeter group of type $\mathrm{A}$.

MSC(Primary)	19A22
MSC(Secondary)	20F55;
Uncontrolled Keywords	Burnside ring; Coxeter group; unit group; parabolic subgroup;

COIMBRA CHARÃO, Ruy; IKEHATA, Ryo;

Note on asymptotic profile of solutions to the linearized compressible Navier-Stokes flow.

Hokkaido Mathematical Journal, 48 (2019) pp.357-383

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Abstract

We consider the asymptotic behavior as $t \to +\infty$ of the $L^{2}$-norm of the velocity of the linearized compressible Navier-Stokes equations in ${\bf R}^{n}$ ($n \geq 2$). As an application we shall study the optimality of the decay rate for the $L^{2}$-norm of the velocity by deriving a decay estimate from below as $t \to +\infty$. To get the estimates in the zone of high frequency we use a version of the energy method in the Fourier space combined with the Haraux-Komornik inequality and this seems much different from known techniques to study compressible Navier-Stokes system.

MSC(Primary)	35Q30
MSC(Secondary)	35B40; 76N99; 35C20;
Uncontrolled Keywords	Compressible Navier-Stokes equations; Cauchy problem; Asymptotic profiles; Weighted $L^{1}$-initial data; Low and high frequencies;

INOGUCHI, Jun-ichi; NAITOH, Hiroo;

Grassmann geometry on the 3-dimensional non-unimodular Lie groups.

Hokkaido Mathematical Journal, 48 (2019) pp.385-406

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Abstract

We study the Grassmann geometry of surfaces when the ambient space is a 3-dimensional non-unimodular Lie group with left invariant metric. This work together with our previous papers yield a complete classification of Grassmann geometry of orbit type in all 3-dimensional homogeneous spaces.

MSC(Primary)	53B25
MSC(Secondary)	53C40; 53C30;
Uncontrolled Keywords	Grassmann geometry; non-unimodular Lie group;

SRIVASTAVA, H. M.; KHAN, Bilal; KHAN, Nazar; AHMAD, Qazi Zahoor;

Coefficient inequalities for $q$-starlike functions associated with the Janowski functions.

Hokkaido Mathematical Journal, 48 (2019) pp.407-425

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Abstract

The main purpose of this investigation is to find several coefficient inequalities and a sufficient condition for $q$-starlike functions which are associated with the Janowski functions. Relevant connections of the results presented in this paper with those in a number of other related works on this subject are also pointed out.

MSC(Primary)	05A30
MSC(Secondary)	30C45; 11B65; 47B38;
Uncontrolled Keywords	Analytic functions; Univalent functions; Convex and $q$-convex functions; Starlike and $q$-starlike functions; $q$-Derivative operator; Basic (or $q$-) hypergeometric functions;

SHI, Qingsong; ADACHI, Toshiaki;

Comparison theorems on trajectory-harps for Kähler magnetic fields which are holomorphic at their arches.

Hokkaido Mathematical Journal, 48 (2019) pp.427-441

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Abstract

A trajectory-harp is a variation of geodesics associated with a trajectory. We estimate how trajectories for Kähler magnetic fields go away from their initial points and show how they are bended by comparing trajectory-harps on a Kähler manifolds with those on complex space forms. Under a condition on sectional curvatures, we show that when the length of a geodesic segment of a trajectory-harp coincides with that on a complex space form it forms a part of a totally geodesic complex line.

MSC(Primary)	53C22
MSC(Secondary)	53B35;
Uncontrolled Keywords	Kähler magnetic fields; trajectory-harps; string-length; string-cosine; zenith angles;

KIM, Yoenha; KO, Eungil; LEE, Jongrak; NAKAZI, Takahiko;

Hyponormality of singular Cauchy integral operators with matrix-valued symbols.

Hokkaido Mathematical Journal, 48 (2019) pp.443-459

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Abstract

In this paper, we study a class of hyponormal singular integral operators with matrix-valued symbols. First, we characterize hyponormal singular integral operators $S_{\Phi,\Psi}$ with trigonometric polynomial symbols $\Phi$ and $\Psi$. Next, we concentrate on the hyponormality of $S_{\Phi,\Psi}$ with some assumptions for the symbols $\Phi$ and $\Psi$.

MSC(Primary)	45E10
MSC(Secondary)	47B35; 47B20;
Uncontrolled Keywords	singular integral operator; Hardy space; hyponormal operator; block Toeplitz operators;