Hokkaido Mathematical Journal

No. 1

CARDONA, Duván; RUZHANSKY, Michael;

Hörmander condition for pseudo-multipliers associated to the harmonic oscillator.

Hokkaido Mathematical Journal, 54 (2025) pp.1-51

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Abstract

In this paper we prove Hörmander-Mihlin multiplier theorems for pseudo-multipliers associated to the harmonic oscillator (also called the Hermite operator). Our approach can be extended to also obtain the $L^p$-boundedness results for multilinear pseudo-multipliers. By using the Littlewood-Paley theorem associated to the harmonic oscillator we also give $L^p$-boundedness and $L^p$-compactness properties for multipliers. $(L^p,L^q)$-estimates for spectral pseudo-multipliers also are investigated.

Keywords	Pseudo-multiplier; Harmonic oscillator; Hermite functions; Hörmander condition; Multilinear operator; Fourier multipliers;
msc2020(primary)	81Q10;
msc2020(secondary)	42C10;

IIYORI, Nobuo; SAWABE, Masato;

$d$-covers of posets of nilpotent subgroups.

Hokkaido Mathematical Journal, 54 (2025) pp.53-69

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Abstract

Let $G$ be a finite group and $n$ a positive integer. Denote by ${\mathcal N}(G,n)$ the totality of non-trivial nilpotent subgroups $H$ of $G$ such that the exponent $\exp(H)$ of $H$ divides $n$. Then we introduce the notion of $d$-covers of ${\mathcal N}(G,n)$. In this paper, we especially investigate in detail 1- and 2-covers of ${\mathcal N}(G,n)$ which reflect the structure of the complex ${\mathcal N}(G,n)$ and the group $G$.

Keywords	nilpotent subgroup; exponent; poset; homotopy equivalence;
msc2020(primary)	20E15;
msc2020(secondary)	20D15; 55U10;

SHI, Yaozhong;

Rigidity of Teichmüller space for geometric intersection number.

Hokkaido Mathematical Journal, 54 (2025) pp.71-85

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Abstract

Since Teichmüller space is a subspace of geodesic current space, the geometric intersection number on geodesic current space is restricted to Teichmüller space. In this paper, we study the rigidity of the Teichmüller space for geometric intersection number. Precisely, we prove that every automorphism of the Teichmüller space with respect to geometric intersection number is induced by an element of the extended mapping class group.

Keywords	Rigidity; Teichmüller space; Geometric intersection number; Geodesic current;
msc2020(primary)	30F60; 32G15; 57M50;

YAMAGUCHI, Hiroshi;

A Bochner type theorem on certain compact groups.

Hokkaido Mathematical Journal, 54 (2025) pp.87-95

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Abstract

The F. and M. Riesz theorem on the circle group was extended, by S. Bochner, to the n-dimensional circle group. S. Saeki gave an extension of the theorem of S. Bochner. On the other hand, Asmar, Montgomery-Smith and Saeki gave a generalization of the Bochner on LCA groups with certain ordered duals. We give a Bochner type theorem on certain noncommutative compact groups.

Keywords	compact group; dual object; measure; Fourier transform; analytic type;
msc2020(primary)	43A05; 43A25; 43A30;

TRUONG, Le Xuan; DO, Tan Duc;

Stability of semigroups generated by degenerate elliptic operators.

Hokkaido Mathematical Journal, 54 (2025) pp.97-133

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Abstract

Let $d \in \{3,4,5,\ldots\}$. We present two quantitative stability results for the $C_0$-semigroup on $L^2_w(\mathds{R}^d)$ generated by the degenerate elliptic operator of the form $$ L = -\frac{1}{w} \operatorname{div}(A \, \nabla u). $$ The weight $w$ belongs to the Muckenhoupt class $A_2$.

Keywords	Degenerate elliptic operator; Muckenhoupt weight; Stability; Quantitative bounds;
msc2020(primary)	35J70; 35K08; 35B35;

ITO, Yohei;

Irregular Riemann-Hilbert Correspondence and Enhanced Subanalytic Sheaves.

Hokkaido Mathematical Journal, 54 (2025) pp.135-169

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Abstract

In [Ito21b], the author explained a relation between enhanced ind-sheaves and enhanced subanalytic sheaves. In this paper, we shall define $\mathbb{C}$-constructibility for enhanced subanalytic sheaves which was announced in [Ito21b, Remark 3.42], and show that there exists an equivalence of categories between the triangulated category of $\mathbb{C}$-constructible enhanced subanalytic sheaves and the one of holonomic $\mathcal{D}$-modules.

Keywords	Irregular Riemann-Hilbert correspondence; D-modules; subanalytic sheaves; ind-sheaves;
msc2020(primary)	18F10; 32C38; 35Q15; 32S60;

YAMASHITA, Go;

Twisted Heilbronn virtual characters.

Hokkaido Mathematical Journal, 54 (2025) pp.171-184

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Abstract

We introduce a twisted version of Heilbronn virtual characters and show twisted versions of the results of Heilbronn, Stark, and Foote-Murty on the holomorphicity and the zeros of Artin $L$-functions. The method of the proofs is similar as the one in the untwisted cases except that we use a theorem in the finite group theory as a new ingredient in the theory of Heilbronn virtual characters.

Keywords	Artin L-function; Artin conjecture; zeros and poles in the critical strip; Heilbronn character; finite group theory;
msc2020(primary)	11R42; 11M26; 20F16;