All issues
Volume 61 (2009)
- Issue 4 Pages 971-
- Issue 3 Pages 651-
- Issue 2 Pages 327-
- Issue 1 Pages 1-
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-Butsurigaku Kwai Kiji
- Tokyo Sugaku Kaisya Zasshi
Volume 61, Issue 1
Displaying 1-12 of 12 articles from this issue
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Katrin Schumacher2009Volume 61Issue 1 Pages 1-38
Published: 2009
Released on J-STAGE: February 23, 2009
JOURNAL FREE ACCESSWe investigate the stationary Navier-Stokes equations in Bessel-potential spaces with Muckenhoupt weights. Since in this setting it is possible that the solutions do not posses any weak derivatives, we use the notation of very weak solutions introduced by Amann [1]. The basic tool is complex interpolation, thus we give a characterization of the interpolation spaces of the spaces of data and solutions. Then we establish a theory of solutions to the Stokes equations in weighted Bessel-potential spaces and use this to prove solvability of the Navier-Stokes equations for small data by means of Banach's Fixed Point Theorem.View full abstractDownload PDF (361K) -
Dedicated to Professor Kenji Yajima on his sixtieth birthdayNaoyasu Kita, Akihiro Shimomura2009Volume 61Issue 1 Pages 39-64
Published: 2009
Released on J-STAGE: February 23, 2009
JOURNAL FREE ACCESSWe study the asymptotic behavior in time of solutions to the Cauchy problem of nonlinear Schrödinger equations with a long-range dissipative nonlinearity given by λ |u|p-1u in one space dimension, where 1 < p ≤ 3 (namely, p is a critical or subcritical exponent) and λ is a complex constant satisfying Im λ < 0 and ((p-1)/2√p) |Re λ| ≤ |Im λ|. We present the time decay estimates and the large-time asymptotics of the solution for arbitrarily large initial data, when “p = 3” or &ladquo;p < 3 and p is suitably close to 3”.View full abstractDownload PDF (271K) -
Virginie Bonnaillie-Noël, Francis Nier, Yassine Patel2009Volume 61Issue 1 Pages 65-106
Published: 2009
Released on J-STAGE: February 23, 2009
JOURNAL FREE ACCESSThis article continues the asymptotic analysis of a nonlinear Schrödinger-Poisson system which models in a far from equilibrium regime the quantum transport in electronic devices like resonant tunneling diodes. Within the reduction to an h-dependent linear problem with uniform regularity estimates for the potential already established in the first part, explicit computations of the asymptotic finite dimensional nonlinear system are derived. They rely on an accurate (phase-space) analysis of the tunnel effect which relies on some kind of Breit-Wigner formula and Fermi golden rule.View full abstractDownload PDF (407K) -
Ryushi Goto2009Volume 61Issue 1 Pages 107-132
Published: 2009
Released on J-STAGE: February 23, 2009
JOURNAL FREE ACCESSLet X be a compact Kähler manifolds with a non-trivial holomorphic Poisson structure β. Then there exist deformations {(\mathscr{J}βt, ψt)} of non-trivial generalized Kähler structures with one pure spinor on X. We prove that every Poisson submanifold of X is a generalized Kähler submanifold with respect to (\mathscr{J}βt, ψt) and provide non-trivial examples of generalized Kähler submanifolds arising as holomorphic Poisson submanifolds. We also obtain unobstructed deformations of bihermitian structures constructed from Poisson structures.View full abstractDownload PDF (324K) -
Degenerate integrodifferential equations of parabolic type with Robin boundary conditions: L2-theoryAngelo Favini, Alfredo Lorenzi, Hiroki Tanabe2009Volume 61Issue 1 Pages 133-176
Published: 2009
Released on J-STAGE: February 23, 2009
JOURNAL FREE ACCESSThis paper is devoted to solving a degenerate parabolic integrodifferential equation with the Robin boundary condition. We begin with solving the equation without the integral delay term. For that purpose we introduce some new unknown function following Favini and Yagi [4] and construct the fundamental solution to the equation to be satisfied by it by the method of Kato and Tanabe [5]. Using this fundamental solution we transform the original problem to an easily solvable integral equation for the time derivative of the new unknown function.View full abstractDownload PDF (292K) -
Shu Nakamura2009Volume 61Issue 1 Pages 177-211
Published: 2009
Released on J-STAGE: February 23, 2009
JOURNAL FREE ACCESSWe consider Schrödinger equations with variable coefficients, which are long-range type perturbations of the flat Laplacian on Rn. We characterize the wave front set of solutions to Schrödinger equations in terms of the initial state. Then it is shown that the singularities propagates along the classical flow, and results are formulated in a semiclassical setting. Methods analogous to the long-range scattering theory, in particular a modified free propagator, are employed.View full abstractDownload PDF (306K) -
Boo Rim Choe2009Volume 61Issue 1 Pages 213-224
Published: 2009
Released on J-STAGE: February 23, 2009
JOURNAL FREE ACCESSD. Luecking has recently proved that a Toeplitz operator with measure symbol on the Bergman space of unit disk has finite rank if and only if its symbols is a linear combination of point masses. In this note we extend this theorem to higher dimensional cases.View full abstractDownload PDF (199K) -
Hyungwoon Koo, Kyesook Nam, HeungSu Yi2009Volume 61Issue 1 Pages 225-235
Published: 2009
Released on J-STAGE: February 23, 2009
JOURNAL FREE ACCESSOn the setting of the upper half-space H of the Euclidean n-spaces, we give a sharp norm estimate of the weighted harmonic Bergman projection on Lpα for 1 < p < ∞. Also, we obtain the norm estimate of the projection depending on α > -1 when p is fixed.View full abstractDownload PDF (204K) -
Pieter C. Allaart2009Volume 61Issue 1 Pages 237-262
Published: 2009
Released on J-STAGE: February 23, 2009
JOURNAL FREE ACCESSThis paper considers a class of continuous functions constructed as a series of iterates of the ``tent map'' multiplied by variable signs. This class includes Takagi's nowhere-differentiable function, and contains the functions studied by Hata and Yamaguti [Japan J. Appl. Math., 1 (1984), 183-199] and Kono [Acta Math. Hungar., 49 (1987), 315-324] as a proper subclass. A complete description is given of the differentiability properties of the functions in this class, and several statements are proved concerning their uniform and local moduli of continuity. The results are applied to generation of random functions.View full abstractDownload PDF (312K) -
Kouji Yamamuro2009Volume 61Issue 1 Pages 263-289
Published: 2009
Released on J-STAGE: February 23, 2009
JOURNAL FREE ACCESSA definition of Lévy processes with values in the space of probability measures was introduced by Shiga and Tanaka (Electronic J. Prob. 11 (2006)). It is shown that the Lévy process with values in the space of probability measures in law has a modification satisfying a certain condition. The modification is a Lévy process in the sense of Shiga and Tanaka. The Lévy-Itô decomposition of sample paths of the Lévy process satisfying the condition is derived.View full abstractDownload PDF (281K) -
Tapani Matala-aho2009Volume 61Issue 1 Pages 291-313
Published: 2009
Released on J-STAGE: February 23, 2009
JOURNAL FREE ACCESSWe shall consider linear independence measures for the values of the functions Da(z) and Ea(z) given below, which can be regarded as q-analogues of Euler's divergent series and the usual exponential series. For the q-exponential function Eq(z), our main result (Theorem 1) asserts the linear independence (over any number field) of the values 1 and Eq(αz) (j = 1,…,m) together with its measure having the exponent μ = O (m), which sharpens the known exponent μ = O (m2) obtained by a certain refined version of Siegel's lemma (cf. [1]). Let p be a prime number. Then Theorem 1 further implies the linear independence of the p-adic numbers ∏n=1∞ (1+kpn), (k = 0,1,…,p-1), over Q with its measure having the exponent μ < 2p. Our proof is based on a modification of Maier's method which allows to construct explicit Padé type approximations (of the second kind) for certain q-hypergeometric series.View full abstractDownload PDF (274K) -
Sadahiro Maeda, Toshiaki Adachi, Young Ho Kim2009Volume 61Issue 1 Pages 315-325
Published: 2009
Released on J-STAGE: February 23, 2009
JOURNAL FREE ACCESSIt is well-known that there exist no homogeneous ruled real hypersurfaces in a complex projective space. On the contrary there exists the unique homogeneous ruled real hypersurface in a complex hyperbolic space. Moreover, it is minimal. We characterize geometrically this minimal homogeneous real hypersurface by properties of extrinsic shapes of some curves.View full abstractDownload PDF (200K)
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