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Journal of the Mathematical Society of Japan
- Vol.69(2017)
  - No.2 p.459-
  - No.1 p.1-
- Vol.68(2016)
- Vol.67(2015)
- Vol.66(2014)
- Vol.65(2013)
- Vol.64(2012)
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- Vol.55(2003)
- Vol.54(2002)
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- Vol.52(2000)
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- Vol.50(1998)
- Vol.49(1997)
- Vol.48(1996)
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- Vol.43(1991)
- Vol.42(1990)
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- Vol.5(1953)
- Vol.4(1952)
- Vol.3(1951)
  - No.2 p.259-
  - No.1 p.1-
- Vol.2(1950 - 1951)
  - No.3-4 p.1･･･
  - No.1-2 p.1-
- Vol.1(1948 - 1950)

Predecessor

Proceedings of the Physico-Mathematical Society of Japan. 3rd Series

Proceedings of the Tokyo Mathematico-Physical Society. 2nd Series

Tokyo Sugaku-Butsurigakukwai Kiji-Gaiyo

Tokyo Sugaku-Butsurigakkwai Hokoku

Tokyo Sugaku-Butsurigaku Kwai Kiji

Tokyo Sugaku Kaisya Zasshi

Journal of the Mathematical Society of Japan Vol. 69(2017) No. 2

On sharp bilinear Strichartz estimates of Ozawa–Tsutsumi type

Jonathan Bennett, Neal Bez, Chris Jeavons, Nikolaos Pattakos

Released: May 12, 2017

p.459-476

We provide a comprehensive analysis of sharp bilinear estimates of Ozawa–Tsutsumi type for solutions u of the free Schrödinger equation, which give sharp control on |u|² in classical Sobolev spaces. In particular, we generalise their estimates in such a way that provides a unification with some sharp bilinear estimates proved by Carneiro and Planchon–Vega, via entirely different methods, by seeing them all as special cases of a one-parameter family of sharp estimates. The extremal functions are solutions of the Maxwell–Boltzmann functional equation and hence Gaussian. For u² we argue that the natural analogous results involve certain dispersive Sobolev norms; in particular, despite the validity of the classical Ozawa–Tsutsumi estimates for both |u|² and u² in the classical Sobolev spaces, we show that Gaussians are not extremisers in the latter case for spatial dimensions strictly greater than two.

Value distribution of leafwise holomorphic maps on complex laminations by hyperbolic Riemann surfaces

Atsushi Atsuji

Released: May 12, 2017

p.477-501

We discuss the value distribution of Borel measurable maps which are holomorphic along leaves of complex laminations. In the case of complex lamination by hyperbolic Riemann surfaces with an ergodic harmonic measure, we have a defect relation appearing in Nevanlinna theory. It gives a bound of the number of omitted hyperplanes in general position by those maps.

On products in a real moment-angle manifold

Li Cai

Released: May 12, 2017

p.503-528

In this paper we give a necessary and sufficient condition for a (real) moment-angle complex to be a topological manifold. The cup and cap products in a real moment-angle manifold are studied. Consequently, the cohomology ring (with coefficients integers) of a polyhedral product by pairs of disks and their bounding spheres is isomorphic to that of a differential graded algebra associated to K and the dimensions of the disks.

Multilinear Fourier multipliers with minimal Sobolev regularity, II

Loukas Grafakos, Akihiko Miyachi, Hanh van Nguyen, Naohito Tomita

Released: May 12, 2017

p.529-562

We provide characterizations for boundedness of multilinear Fourier multiplier operators on Hardy or Lebesgue spaces with symbols locally in Sobolev spaces. Let H^q(ℝⁿ) denote the Hardy space when 0 < q ≤ 1 and the Lebesgue space L^q(ℝⁿ) when 1 < q ≤ ∞. We find optimal conditions on m-linear Fourier multiplier operators to be bounded from H^p₁ × … × H^p_m to L^p when 1/p = 1/p₁ + … + 1/p_m in terms of local L²-Sobolev space estimates for the symbol of the operator. Our conditions provide multilinear analogues of the linear results of Calderón and Torchinsky [1] and of the bilinear results of Miyachi and Tomita [17]. The extension to general m is significantly more complicated both technically and combinatorially; the optimal Sobolev space smoothness required of the symbol depends on the Hardy–Lebesgue exponents and is constant on various convex simplices formed by configurations of m2^m−1 + 1 points in [0,∞)^m.

An example of Schwarz map of reducible Appell's hypergeometric equation E₂ in two variables

Keiji Matsumoto, Takeshi Sasaki, Tomohide Terasoma, Masaaki Yoshida

Released: May 12, 2017

p.563-595

We study an Appell hypergeometric system E₂ of rank four which is reducible, and show that its Schwarz map admits geometric interpretations: the map can be considered as the universal Abel–Jacobi map of a 1-parameter family of curves of genus 2.

Dimension formulas of paramodular forms of squarefree level and comparison with inner twist

Tomoyoshi Ibukiyama, Hidetaka Kitayama

Released: May 12, 2017

p.597-671

In this paper, we give an explicit dimension formula for the spaces of Siegel paramodular cusp forms of degree two of squarefree level. As an application, we propose a conjecture on symplectic group version of Eichler–Jacquet–Langlands type correspondence. It is a generalization of the previous conjecture of the first named author for prime levels published in 1985, where inner twists corresponding to binary quaternion hermitian forms over definite quaternion algebras were treated. Our present study contains also the case of indefinite quaternion algebras. Additionally, we give numerical examples of L functions which support the conjecture. These comparisons of dimensions and examples give also evidence for conjecture on a certain precise lifting theory. This is related to the lifting theory from pairs of elliptic cusp forms initiated by Y. Ihara in 1964 in the case of compact twist, but no such construction is known in the case of non-split symplectic groups corresponding to quaternion hermitian groups over indefinite quaternion algebras and this is new in that sense.

Asymptotic expansion of resolvent kernels and behavior of spectral functions for symmetric stable processes

Masaki Wada

Released: May 12, 2017

p.673-692

We give a precise behavior of spectral functions for symmetric stable processes applying the asymptotic expansion of resolvent kernels.

Pseudograph and its associated real toric manifold

Suyoung Choi, Boram Park, Seonjeong Park

Released: May 12, 2017

p.693-714

Given a simple graph G, the graph associahedron P_G is a convex polytope whose facets correspond to the connected induced subgraphs of G. Graph associahedra have been studied widely and are found in a broad range of subjects. Recently, S. Choi and H. Park computed the rational Betti numbers of the real toric variety corresponding to a graph associahedron under the canonical Delzant realization. In this paper, we focus on a pseudograph associahedron which was introduced by Carr, Devadoss and Forcey, and then discuss how to compute the Poincaré polynomial of the real toric variety corresponding to a pseudograph associahedron under the canonical Delzant realization.

A note on bounded-cohomological dimension of discrete groups

Clara Löh

Released: May 12, 2017

p.715-734

Bounded-cohomological dimension of groups is a relative of classical cohomological dimension, defined in terms of bounded cohomology with trivial coefficients instead of ordinary group cohomology. We will discuss constructions that lead to groups with infinite bounded-cohomological dimension, and we will provide new examples of groups with bounded-cohomological dimension equal to 0. In particular, we will prove that every group functorially embeds into an acyclic group with trivial bounded cohomology.

Cartan matrices and Brauer's k(B)-conjecture IV

Benjamin Sambale

Released: May 12, 2017

p.735-754

In this note we give applications of recent results coming mostly from the third paper of this series. It is shown that the number of irreducible characters in a p-block of a finite group with abelian defect group D is bounded by |D| (Brauer's k(B)-conjecture) provided D has no large elementary abelian direct summands. Moreover, we verify Brauer's k(B)-conjecture for all blocks with minimal non-abelian defect groups. This extends previous results by various authors.

The category of reduced orbifolds in local charts

Anke D. Pohl

Released: May 12, 2017

p.755-800

It is well-known that reduced smooth orbifolds and proper effective foliation Lie groupoids form equivalent categories. However, for certain recent lines of research, equivalence of categories is not sufficient. We propose a notion of maps between reduced smooth orbifolds and a definition of a category in terms of marked proper effective étale Lie groupoids such that the arising category of orbifolds is isomorphic (not only equivalent) to this groupoid category.

Lifting puzzles and congruences of Ikeda and Ikeda–Miyawaki lifts

Neil Dummigan

Released: May 12, 2017

p.801-818

We show how many of the congruences between Ikeda lifts and non-Ikeda lifts, proved by Katsurada, can be reduced to congruences involving only forms of genus 1 and 2, using various liftings predicted by Arthur's multiplicity conjecture. Similarly, we show that conjectured congruences between Ikeda–Miyawaki lifts and non-lifts can often be reduced to congruences involving only forms of genus 1, 2 and 3.

Contact of a regular surface in Euclidean 3-space with cylinders and cubic binary differential equations

Toshizumi Fukui, Masaru Hasegawa, Kouichi Nakagawa

Released: May 12, 2017

p.819-847

We investigate the contact types of a regular surface in the Euclidean 3-space ℝ³ with right circular cylinders. We present the conditions for existence of cylinders with A₁, A₂, A₃, A₄, A₅, D₄, and D₅ contacts with a given surface. We also investigate the kernel field of A_≥3-contact cylinders on the surface. This is defined by a cubic binary differential equation and we classify singularity types of its flow in the generic context.

Integral transformation of Heun's equation and some applications

Kouichi Takemura

Released: May 12, 2017

p.849-891

It is known that the Fuchsian differential equation which produces the sixth Painlevé equation corresponds to the Fuchsian differential equation with different parameters via Euler's integral transformation, and Heun's equation also corresponds to Heun's equation with different parameters, again via Euler's integral transformation. In this paper we study the correspondences in detail. After investigating correspondences with respect to monodromy, it is demonstrated that the existence of polynomial-type solutions corresponds to apparency of a singularity. For the elliptical representation of Heun's equation, correspondence with respect to monodromy implies isospectral symmetry. We apply the symmetry to finite-gap potentials and express the monodromy of Heun's equation with parameters which have not yet been studied.

1 - 14 / 14 Articles.

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Back Issues

Volume And Issue List
Journal of the Mathematical Society of Japan

Predecessor

Journal of the Mathematical Society of Japan Vol. 69(2017) No. 2

On sharp bilinear Strichartz estimates of Ozawa–Tsutsumi type

Value distribution of leafwise holomorphic maps on complex laminations by hyperbolic Riemann surfaces

On products in a real moment-angle manifold

Multilinear Fourier multipliers with minimal Sobolev regularity, II

An example of Schwarz map of reducible Appell's hypergeometric equation E₂ in two variables

Dimension formulas of paramodular forms of squarefree level and comparison with inner twist

Asymptotic expansion of resolvent kernels and behavior of spectral functions for symmetric stable processes

Pseudograph and its associated real toric manifold

A note on bounded-cohomological dimension of discrete groups

Cartan matrices and Brauer's k(B)-conjecture IV

The category of reduced orbifolds in local charts

Lifting puzzles and congruences of Ikeda and Ikeda–Miyawaki lifts

Contact of a regular surface in Euclidean 3-space with cylinders and cubic binary differential equations

Integral transformation of Heun's equation and some applications

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Volume And Issue List Journal of the Mathematical Society of Japan

Predecessor

Journal of the Mathematical Society of Japan Vol. 69(2017) No. 2

System Maintenance

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Journal Tools

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Volume And Issue List
Journal of the Mathematical Society of Japan