Kyushu Journal of Mathematics

STABILITY OF RAREFACTION WAVES FOR A MODEL SYSTEM OF A RADIATING GAS

Shuichi KAWASHIMA, Yoshihito TANAKA

2004 Volume 58 Issue 2 Pages 211-250
Published: 2004
Released on J-STAGE: March 24, 2005

DOIhttps://doi.org/10.2206/kyushujm.58.211

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ZEROS OF EISENSTEIN SERIES

Winfried KOHNEN

2004 Volume 58 Issue 2 Pages 251-256
Published: 2004
Released on J-STAGE: March 24, 2005

DOIhttps://doi.org/10.2206/kyushujm.58.251

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RANDOM BOUNDED OPERATORS AND THEIR EXTENSION

Dang Hung THANG, Nguyen THINH

2004 Volume 58 Issue 2 Pages 257-276
Published: 2004
Released on J-STAGE: March 24, 2005

DOIhttps://doi.org/10.2206/kyushujm.58.257

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In this paper, the random bounded operators from a Banach space X into a Banach space Y and the problem of extending random operators are investigated. It is shown that unlike the deterministic bounded operators, the random version of the principle of uniform boundedness and the Banach-Steinhaus theorem do not hold for random bounded operators. In addition, a random operator can be extended to apply to all random inputs if and only if it is bounded. As a consequence, we conclude that the Ito stochastic integral cannot be extended in a natural fashion to all random functions with square-integrable sample paths.

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ON THE SPECTRUM AND THE LOWEST EIGENVALUE OF CERTAIN NON-COMMUTATIVE HARMONIC OSCILLATORS

Alberto PARMEGGIANI

2004 Volume 58 Issue 2 Pages 277-322
Published: 2004
Released on J-STAGE: March 24, 2005

DOIhttps://doi.org/10.2206/kyushujm.58.277

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We study here various expansions and approximations of the spectrum of non-commutative harmonic oscillators of the type
Q (x, D_x) = A (−∂_x²/2 + x²/2) + B (x∂_x + 1/2), x ∈ R,
where A, B are constant 2 × 2 matrices such that A is real symmetric positive (or negative) definite and B ≠ 0 is real skew-symmetric, when the Hermitian matrix A + iB is positive (or negative) definite. Special emphasis is put on the lowest eigenvalue. These expansions are written in terms of det(A )/pf(B )² in the limit det(A ) → +∞ for constant pf(B ) and constant Tr(A )/√det(A ).

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DIFFERENTIAL EQUATIONS FOR INVARIANT CURVES UNDER KLEIN'S SIMPLE GROUP OF ORDER 168

Mitsuo KATO

2004 Volume 58 Issue 2 Pages 323-336
Published: 2004
Released on J-STAGE: March 24, 2005

DOIhttps://doi.org/10.2206/kyushujm.58.323

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SELBERG ZETA FUNCTIONS OF INFINITE SYMMETRIC GROUPS

Kazufumi KIMOTO

2004 Volume 58 Issue 2 Pages 337-352
Published: 2004
Released on J-STAGE: March 24, 2005

DOIhttps://doi.org/10.2206/kyushujm.58.337

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The main purpose of this paper is to seek a reasonable formulation of Selberg zeta functions of infinite symmetric groups and calculate actual candidates of them. In order to achieve this, we introduce a (Selberg-type) zeta function attached to a finite group action G ?? X. As candidates of Selberg zeta functions of the infinite symmetric group ?? _∞, we calculate a (normalized) limit of the zeta functions of finite symmetric group actions. We also show that this zeta function is a generating function of certain quantities called moments of the action, which determine the multiple transitivity of group actions.

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ON THE FIRST SUBCONSTITUENT OF A QUADRATIC FORMS SCHEME

Seiichi IWAMOTO

2004 Volume 58 Issue 2 Pages 353-371
Published: 2004
Released on J-STAGE: March 24, 2005

DOIhttps://doi.org/10.2206/kyushujm.58.353

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As a step to find the eigenvalues of the first subconstituent X₁ of a quadratic forms scheme, we determine the orbits of GL_n(q ) acting on X₁ × X₁.

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EXISTENCE OF GLOBAL SOLUTIONS FOR THE KIRCHHOFF-TYPE QUASILINEAR WAVE EQUATION IN EXTERIOR DOMAINS WITH A HALF-LINEAR DISSIPATION

Mitsuhiro NAKAO

2004 Volume 58 Issue 2 Pages 373-391
Published: 2004
Released on J-STAGE: March 24, 2005

DOIhttps://doi.org/10.2206/kyushujm.58.373

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AN AUGMENTATION OF THE PHASE SPACE OF THE SYSTEM OF TYPE A₄⁽¹⁾

Nobuhiko TAHARA

2004 Volume 58 Issue 2 Pages 393-425
Published: 2004
Released on J-STAGE: March 24, 2005

DOIhttps://doi.org/10.2206/kyushujm.58.393

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We investigate the differential system with affine Weyl group symmetry of type A₄⁽¹⁾ and construct a space which parametrizes all meromorphic solutions of it. To demonstrate our method based on singularity analysis and affine Weyl group symmetry, we first study the system of type A₂⁽¹⁾, which is the equivalent of the fourth Painlevé equation, and obtain the space which augments the original phase space of the system by adding spaces of codimension 1. For the system of type A₄⁽¹⁾, codimension 2 spaces should be added to the phase space of the system in addition to codimension 1 spaces.

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