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Volume 63 (2011)
- Issue 4 Pages 1085-
- Issue 3 Pages 715-
- Issue 2 Pages 363-
- 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 63, Issue 1
Displaying 1-11 of 11 articles from this issue
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Setsuro Fujiié, Amina Lahmar-Benbernou, André Martinez2011 Volume 63 Issue 1 Pages 1-78
Published: 2011
Released on J-STAGE: February 25, 2011
JOURNAL FREE ACCESSWe consider the semiclassical Schrödinger operator with a well in an island potential, on which we assume smoothness only, except near infinity. We give the asymptotic expansion of the imaginary part of the shape resonance at the bottom of the well. This is a generalization of the result by Helffer and Sjöstrand [HeSj1] in the globally analytic case. We use an almost-analytic extension in order to continue the WKB solution coming from the well beyond the caustic set, and, for the justification of the accuracy of this approximation, we develop some refined microlocal arguments in h-dependent small regions.View full abstractDownload PDF (501K) -
Jörg Brendle, Benedikt Löwe2011 Volume 63 Issue 1 Pages 137-151
Published: 2011
Released on J-STAGE: February 25, 2011
JOURNAL FREE ACCESSIn this paper, we are considering the Baire property of the eventually different topology as a regularity property for sets of reals and investigate the logical strength of the statements “Every Δ12 set has the Baire property in the eventually different topology” and “Every Σ12 set has the Baire property in the eventually different topology”. The latter statement turns out to be equivalent to “ω1 is inaccessible by reals”.View full abstractDownload PDF (308K) -
Fumiya Morishita, Osamu Saeki2011 Volume 63 Issue 1 Pages 153-162
Published: 2011
Released on J-STAGE: February 25, 2011
JOURNAL FREE ACCESSFor a given closed surface, we study height functions with three critical values associated with immersions of the surface into 3-space, where the critical points may not be non-degenerate. We completely characterize the numbers of critical points corresponding to the three critical values that can be realized by such height functions. We also study the cases where the immersion can be replaced by an embedding or the critical points are all non-degenerate. Similar problems are studied for distance functions as well.View full abstractDownload PDF (220K) -
Reinhard Farwig, Šárka Nečasová, Jiř& ...2011 Volume 63 Issue 1 Pages 163-194
Published: 2011
Released on J-STAGE: February 25, 2011
JOURNAL FREE ACCESSWe consider the spectrum of the Stokes operator with and without rotation effect for the whole space and exterior domains in Lq-spaces. Based on similar results for the Dirichlet-Laplacian on Rn, n ≥ 2, we prove in the whole space case that the spectrum as a set in C does not change with q ∈ (1,∞), but it changes its type from the residual to the continuous or to the point spectrum with q. The results for exterior domains are less complete, but the spectrum of the Stokes operator with rotation mainly is an essential one, consisting of infinitely many equidistant parallel half-lines in the left complex half-plane. The tools are strongly based on Fourier analysis in the whole space case and on stability properties of the essential spectrum for exterior domains.View full abstractDownload PDF (338K) -
Satoru Fukasawa2011 Volume 63 Issue 1 Pages 195-209
Published: 2011
Released on J-STAGE: February 25, 2011
JOURNAL FREE ACCESSFor a plane curve, a point in the projective plane is said to be Galois when the point projection induces a Galois extension of function fields. We completely classify plane curves with infinitely many outer Galois points.View full abstractDownload PDF (215K) -
Toshiyuki Kikuta, Shoyu Nagaoka2011 Volume 63 Issue 1 Pages 211-238
Published: 2011
Released on J-STAGE: February 25, 2011
JOURNAL FREE ACCESSWe generalize the notion of modular forms mod p to the case of Hermitian modular forms. Moreover we determine the structure of the algebra of degree 2 Hermitian modular forms mod p in the cases that the corresponding quadratic field is Q($¥sqrt{-1}$) and Q($¥sqrt{-3}$).View full abstractDownload PDF (279K) -
Haruya Mizutani2011 Volume 63 Issue 1 Pages 239-261
Published: 2011
Released on J-STAGE: February 25, 2011
JOURNAL FREE ACCESSWe study the time decay of scattering solutions to one-dimensional Schrödinger equations and prove a weighted dispersive estimate with stronger time decay than the case of unweighted estimates for the non-resonant state. Furthermore asymptotic expansions in time of scattering solutions are given. The key of the proof is the study of the Fourier properties of the Jost functions. We improve the Fourier properties of the Jost functions obtained by D'Ancona and Fanelli [2].View full abstractDownload PDF (252K) -
Ryuji Kajikiya2011 Volume 63 Issue 1 Pages 263-294
Published: 2011
Released on J-STAGE: February 25, 2011
JOURNAL FREE ACCESSA sublinear elliptic equation whose coefficient is singular on the boundary is studied in any bounded domain Ω under the zero Dirichlet boundary condition. It is proved that the equation has a unique positive solution and infinitely many sign-changing solutions which belong to C1($¥overline{¥Omega}$) or C2(¥overline{¥Omega}$). Moreover, it is proved that the solutions have the higher order regularity corresponding to the smoothness of the coefficient.View full abstractDownload PDF (280K) -
Xuan Thinh Duong, Lixin Yan2011 Volume 63 Issue 1 Pages 295-319
Published: 2011
Released on J-STAGE: February 25, 2011
JOURNAL FREE ACCESSLet (X, d, μ) be a metric measure space endowed with a distance d and a nonnegative Borel doubling measure μ. Let L be a non-negative self-adjoint operator on L2(X). Assume that the semigroup e-tL generated by L satisfies the Davies-Gaffney estimates. Let HpL(X) be the Hardy space associated with L. We prove a Hörmander-type spectral multiplier theorem for L on HpL(X) for 0 < p < ∞: the operator m(L) is bounded from HpL(X) to HpL(X) if the function m possesses s derivatives with suitable bounds and s > n (1/p-1/2) where n is the “dimension” of X. By interpolation, m(L) is bounded on HpL(X) for all 0 < p < ∞ if m is infinitely differentiable with suitable bounds on its derivatives. We also obtain a spectral multiplier theorem on Lp spaces with appropriate weights in the reverse Hölder class.View full abstractDownload PDF (294K) -
Raza Lahiani, Carine Molitor-Braun2011 Volume 63 Issue 1 Pages 321-361
Published: 2011
Released on J-STAGE: February 25, 2011
JOURNAL FREE ACCESSLet N be a connected, simply connected nilpotent Lie group with Lie algebra $¥mathfrak{n}$ and let $¥mathscr{W}$ be a submanifold of $¥mathfrak{n}^*$ such that the dimension of all polarizations associated to elements of $¥mathscr{W}$ is fixed. We choose $(¥mathfrak{p}(w))_{w¥in ¥mathscr{W}}$ and $(¥mathfrak{p}'(w))_{w¥in ¥mathscr{W}}$ two smooth families of polarizations in $¥mathfrak{n}$. Let πw = indP(w)Nχw and π′w = indP′(w)Nχw be the corresponding induced representations, which are unitary and irreducible. It is well known that πw and π′w are unitary equivalent. In this paper, we prove the existence of a smooth family of intertwining operator (Tw)w for theses representations, where w runs through an appropriate non-empty relatively open subset of $¥mathscr{W}$. The intertwining operators are given by an explicit formula.View full abstractDownload PDF (382K) -
Osamu Ikawa2011 Volume 63 Issue 1 Pages 79-136
Published: 2011
Released on J-STAGE: February 25, 2011
JOURNAL FREE ACCESSWe introduce the notion of symmetric triad, which is a generalization of the notion of irreducible root system, and study its fundamental properties. Applying these results, we study the orbit spaces of Hermann actions on compact symmetric spaces.View full abstractDownload PDF (387K)
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