Kyushu Journal of Mathematics

THE KYUSHU JOURNAL OF MATHEMATICS VOLUME 60

Masaaki Yoshida

2006 Volume 60 Issue 1 Pages 1
Published: 2006
Released on J-STAGE: August 31, 2006

DOIhttps://doi.org/10.2206/kyushujm.60.1

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ON INTERSECTIONS OF DOMAINS OF UNBOUNDED POSITIVE OPERATORS

Hideki KOSAKI

2006 Volume 60 Issue 1 Pages 3-25
Published: 2006
Released on J-STAGE: August 31, 2006

DOIhttps://doi.org/10.2206/kyushujm.60.3

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We present various examples of pairs (A,B) of (densely defined) positive self-adjoint operators satisfying D(A) ∩ D(B) = 0 and some additional conditions, such as the large intersection of domains of fractional powers.

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MINIMAL SCHWARZ MAPS OF ₃F₂ WITH FINITE IRREDUCIBLE MONODROMY GROUPS

Mitsuo KATO

2006 Volume 60 Issue 1 Pages 27-46
Published: 2006
Released on J-STAGE: August 31, 2006

DOIhttps://doi.org/10.2206/kyushujm.60.27

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The generalized hypergeometric function ₃F₂ (a₀, a₁, a₂; b₁, b₂; z) satisfies the Fuchsian differential equation ₃E₂ of rank three. Beukers and Heckman classified all of the possible parameter sets of ₃E₂ with finite irreducible primitive monodromy groups into 11 classes. In each of these classes, we determine the parameter set of ₃E₂ such that the image curve (in the projective plane) of the Schwarz map defined by the ratio of its three independent solutions attains the minimal degree.

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ON THE CHARACTERISTIC NUMBERS OF THE MANIFOLDS IMMERSED IN THE MULTIPLE POINT SET OF A SELF-TRANSVERSE IMMERSION

Masayoshi KAMATA

2006 Volume 60 Issue 1 Pages 47-62
Published: 2006
Released on J-STAGE: August 31, 2006

DOIhttps://doi.org/10.2206/kyushujm.60.47

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We study characteristic numbers of the manifold immersed in the multiple point set of a self-transverse immersion of a closed manifold in the sphere. The signature of the manifold immersed in the multiple point set is described as the characteristic number with L-classes.

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ALGEBRAIC RELATIONS AMONG SOME THETA FUNCTIONS ON THE BOUNDED SYMMETRIC DOMAIN OF TYPE I_r,r

Keiji MATSUMOTO

2006 Volume 60 Issue 1 Pages 63-77
Published: 2006
Released on J-STAGE: August 31, 2006

DOIhttps://doi.org/10.2206/kyushujm.60.63

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We give algebraic relations among theta functions on the bounded symmetric domain of type I_r,r: quadratic relations among those over the ring Z[i] of Gaussian integers, and over the ring Z[√-2], and cubic relations among those over the ring Z[ω] of Eisenstein integers.

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ON HIGHER-DIMENSIONAL ANALOGUES OF SLEPIAN′S OPERATOR IN HIS BANDWIDTH ARGUMENTS

Atsushi YOSHIKAWA

2006 Volume 60 Issue 1 Pages 79-100
Published: 2006
Released on J-STAGE: August 31, 2006

DOIhttps://doi.org/10.2206/kyushujm.60.79

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Investigations are focused on partial differential operators that commute with certain integral operators analogous to those arising from the communication engineering. An explicit self-adjoint operator is derived for the case of discs in the plane.

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LINE CONGRUENCE AND TRANSFORMATION OF PROJECTIVE SURFACES

Takeshi SASAKI

2006 Volume 60 Issue 1 Pages 101-243
Published: 2006
Released on J-STAGE: August 31, 2006

DOIhttps://doi.org/10.2206/kyushujm.60.101

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The aim of this article is to present and reformulate systematically what is known about surfaces in the projective 3-space, in view of transformations of surfaces, and to complement this with some new results. Special emphasis will be laid on line congruences and Laplace transformations. A line congruence can be regarded as a transformation connecting one focal surface with the other focal surface. A Laplace transformation is regarded as a method of constructing a new surface from a given surface by relying on the asymptotic system the surface is endowed with. A principal object in this article is a class of projectively minimal surfaces. We clarify the procedure of getting new projectively minimal surfaces from a given one, which was found by F. Marcus, as well as the procedure of Demoulin transformation of projective surfaces.

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