Nagoya Mathematical Journal

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Volume 147 - September 1997

Contents

Transforms on white noise functionals with their applications to Cauchy problems
Dong Myung Chung, Un Cig Ji
Published online by Cambridge University Press: 22 January 2016, pp. 1-23
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A generalized Laplacian ΔG (K) is defined as a continuous linear operator acting on the space of test white noise functionals. Operator-parameter - and -transforms on white noise functionals are introduced and then prove a characterization theorem for and -transforms in terms of the coordinate differential operator and the coordinate multiplication. As an application, we investigate the existence and uniqueness of solution of the Cauchy problem for the heat equation associated with ΔG (K)

Semi-classical bounds on scattering cross sections in two dimensional magnetic fields
Hideo Tamura
Published online by Cambridge University Press: 22 January 2016, pp. 25-61
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We prove the uniform boundedness of averaged total cross sections or of quantities related to scattering into cones in the semi-classical limit for scattering by two dimensional magnetic fields. We do not necessarily assume that the energy under consideration is in a non-trapping energy range in the sense of classical dynamics.

A generalization of Kita and Noumi’s vanishing theorems of cohomology groups of local system
Koji Cho
Published online by Cambridge University Press: 22 January 2016, pp. 63-69
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We prove vanishing theorems of cohomology groups of local system, which generalize Kita and Noumi’s result and partially Aomoto’s result. Main ingredients of our proof are the Hodge to de Rham spectral sequence and Serre’s vanishing theorem in algebraic geometry.

Siegel modular forms and theta series attached to quaternion algebras II
S. Böcherer, R. Schulze-Pillot
Published online by Cambridge University Press: 22 January 2016, pp. 71-106
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We continue our study of Yoshida’s lifting, which associates to a pair of automorphic forms on the adelic multiplicative group of a quaternion algebra a Siegel modular form of degree 2. We consider here the case that the automorphic forms on the quaternion algebra correspond to modular forms of arbitrary even weights and square free levels; in particular we obtain a construction of Siegel modular forms of weight 3 attached to a pair of elliptic modular forms of weights 2 and 4.

On the stability of pseudoconvexity for certain covering spaces
Takeo Ohsawa
Published online by Cambridge University Press: 22 January 2016, pp. 107-112
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It is proved that, if is a proper holomorphic map with one-dimensional fibers and a covering map, a point t ∈ T has a neighbourhood U such that is holomorphically convex if and only if is holomorphically convex.

The mixed Hodge structure on the fundamental group of the fiber type 2-arrangement
Yukihito Kawahara
Published online by Cambridge University Press: 22 January 2016, pp. 113-135
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The complement of an arrangement of hyperplanes is a good example of the mixed Hodge structure on the fundamental group of an algebraic variety. We compute its isomorphic class using iterated integrals in the fiber type case and then get the combinatorial and projective invariant.

On plain lattice points whose coordinates are reciprocals modulo a prime
Akio Fujii, Yoshiyuki Kitaoka
Published online by Cambridge University Press: 22 January 2016, pp. 137-146
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We consider, for a given large prime p, the problem of covering a square [0, p] × [0, p] with discs center at the lattice point (x, y), x and y subject to condition xy ≡ 1 (mod p) and with radius r. We are concerned with the size of r.

Sobolev and Lipschitz estimates for weighted Bergman projections
Der-Chen Chang, Bao Qin Li
Published online by Cambridge University Press: 22 January 2016, pp. 147-178
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Let Ω be a bounded, decoupled pseudo-convex domain of finite type in ℂn with smooth boundary. In this paper, we generalize results of Bonami-Grellier [BG] and Bonami-Chang-Grellier [BCG] to study weighted Bergman projections for weights which are a power of the distance to the boundary. We define a class of operators of Bergman type for which we develop a functional calculus. Then we may obtain Sobolev and Lipschitz estimates, both of isotropic and anisotropic type, for these projections.

Cofiniteness of local cohomology modules for ideals of dimension one
Ken-Ichi Yoshida
Published online by Cambridge University Press: 22 January 2016, pp. 179-191
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In this paper, we prove that for any ideal I of dimension one is I-cofinite for all i and for any finite A-module M. Furthermore, for any ideal I over any regular local ring A, we investigate the relationship between I-cofiniteness and vanishing for local cohomology modules .

The genus of curves on the three dimensional quadric
Mark Andrea A. De Cataldo
Published online by Cambridge University Press: 22 January 2016, pp. 193-211
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By means of an ad hoc modification of the so-called “Castelnuovo-Harris analysis” we derive an upper bound for the genus of integral curves on the three dimensional nonsingular quadric which lie on an integral surface of degree 2/c, as a function of k and the degree d of the curve. In order to obtain this we revisit the Uniform Position Principle to make its use computation-free. The curves which achieve this bound can be conveniently characterized.