Japanese journal of mathematics. New series

Stability properties and asymptotic almost periodicity for linear Volterra difference equations in a Banach space

Satoru MURAKAMI, Yutaka NAGABUCHI

2005 年 31 巻 2 号 p. 193-223
発行日: 2005年
公開日: 2008/12/16

DOIhttps://doi.org/10.4099/math1924.31.193

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For linear Volterra difference equations, some stability properties of the zero solution are studied in connection with the summability of the fundamental solution. Also, for perturbed equations with asymptotically almost periodic forcing term, the existence of asymptotically almost periodic solutions is shown under some condition on stabilities.

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Uniform estimates in the velocity at infinity for stationary solutions to the Navier-Stokes exterior problem

Yoshihiro SHIBATA, Masao YAMAZAKI

2005 年 31 巻 2 号 p. 225-279
発行日: 2005年
公開日: 2008/12/16

DOIhttps://doi.org/10.4099/math1924.31.225

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This paper is concerned with the stationary Navier-Stokes equations in exterior domains of dimension n≥3, and provides a sufficient condition on the external force for the unique solvability. This condition is valid both in the case with small but nonzero velocity at infinity, and in the case with zero velocity at infinity. As a result it is proved that, if the external force satisfies this condition, the solution with nonzero velocity at infinity converges to the solution with zero velocity at infinity with respect to the weak-* topology of appropriate function spaces.

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Real Hardy spaces on real rank 1 semisimple Lie groups

Takeshi KAWAZOE

2005 年 31 巻 2 号 p. 281-343
発行日: 2005年
公開日: 2008/12/16

DOIhttps://doi.org/10.4099/math1924.31.281

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Let G be a real rank one connected semisimple Lie group with finite center. We introduce a real Hardy space H¹ (G//K) on G as the space consisting of all K-bi-invariant functions f on G whose radial maximal functions M_φf are integrable on G. We shall obtain a relation between H¹ (G//K) and H¹(R), the real Hardy space on the real line R, via the Abel transform on G and give a characterization of H¹ (G//K).

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On invariants of polynomial functions

Yoshiaki FUKUMA

2005 年 31 巻 2 号 p. 345-378
発行日: 2005年
公開日: 2008/12/16

DOIhttps://doi.org/10.4099/math1924.31.345

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In this paper, we define some invariants of polynomial functions which are derivative from invariants of polarized varieties, and we study their properties. As applications, by using their invariants, we study polarized toric varieties, and we also classify finite partially ordered sets.

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Mean-value estimates for nonlinear Weyl sums over primes

Jianya LIU, Jingmei YE

2005 年 31 巻 2 号 p. 379-390
発行日: 2005年
公開日: 2008/12/16

DOIhttps://doi.org/10.4099/math1924.31.379

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We establish a Bombieri-type mean-value estimate for nonlinear ex-ponential sums over primes. This has applications in the Waring-Goldbach problem.

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Global existence of quasilinear, nonrelativistic wave equations satisfying the null condition

Jason METCALFE, Makoto NAKAMURA, Christopher D. SOGGE

2005 年 31 巻 2 号 p. 391-472
発行日: 2005年
公開日: 2008/12/16

DOIhttps://doi.org/10.4099/math1924.31.391

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We prove global existence of solutions to multiple speed, Dirichlet-wave equations with quadratic nonlinearities satisfying the null condition in the exterior of compact obstacles. This extends the result of our previous paper by allowing general higher order terms. In the currect setting, these terms are much more difficult to handle than for the free wave equation, and we do so using an analog of a pointwise estimate due to Kubota and Yokoyama.

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