1.
Examples of the Hurwitz transform - LI, Hai-Long; HASHIMOTO, Masahiro; KANEMITSU, Shigeru
Espinosa and Moll [2], [3] studied “the Hurwitz transform” meaning an integral over [0, 1] of a Fourier series multiplied by the Hurwitz zeta function $\zeta (z,u)$ , and obtained numerous results for those which arise from the Hurwitz formula. Ito's recent result [4] turns out to be one of the special cases of Espinosa and Moll's theorem. However, they did not give rigorous treatment of the relevant improper integrals.
¶ In this note we shall appeal to a deeper result of Mikolás [9] concerning the integral of the product of two Hurwitz zeta functions and derive all important results of...
3.
Weak extension theorem for measure-preserving homeomorphisms of noncompact manifolds - YAGASAKI, Tatsuhiko
In this paper we deduce weak type extension theorems for the groups of measure-preserving homeomorphisms of noncompact manifolds. As an application, we show that the group of measure-preserving homeomorphisms with compact support of a noncompact connected manifold, endowed with the Whitney topology, is locally contractible.
4.
Weak Harnack inequality for fully nonlinear uniformly elliptic PDE with unbounded ingredients - KOIKE, Shigeaki; ŚWIĘCH, Andrzej
The weak Harnack inequality for $L^{p}$ -viscosity solutions is shown for fully nonlinear, second order uniformly elliptic partial differential equations with unbounded coefficients and inhomogeneous terms. This result extends those of Trudinger for strong solutions [21] and Fok for $L^{p}$ -viscosity solutions [13]. The proof is a modification of that of Caffarelli [5], [6]. We apply the weak Harnack inequality to obtain the strong maximum principle, boundary weak Harnack inequality, global $C^{\alpha}$ estimates for solutions of fully nonlinear equations, strong solvability of extremal equations with unbounded coefficients, and Aleksandrov-Bakelman-Pucci maximum principle in unbounded domains.
5.
Penalising symmetric stable Lévy paths - YANO, Kouji; YANO, Yuko; YOR, Marc
Limit theorems for the normalized laws with respect to two kinds of weight functionals are studied for any symmetric stable Lévy process of index $1 < \alpha \le 2$ . The first kind is a function of the local time at the origin, and the second kind is the exponential of an occupation time integral. Special emphasis is put on the role played by a stable Lévy counterpart of the universal $\sigma $ -finite measure, found in [9] and [10], which unifies the corresponding limit theorems in the Brownian setup for which $\alpha = 2$ .
6.
Asymptotic behavior of flat surfaces in hyperbolic 3-space - KOKUBU, Masatoshi; ROSSMAN, Wayne; UMEHARA, Masaaki; YAMADA, Kotaro
In this paper, we investigate the asymptotic behavior of regular ends of flat surfaces in the hyperbolic $3$ -space $H^{3}$ . Gálvez, Martínez and Milán showed that when the singular set does not accumulate at an end, the end is asymptotic to a rotationally symmetric flat surface. As a refinement of their result, we show that the asymptotic order (called pitch $p$ ) of the end determines the limiting shape, even when the singular set does accumulate at the end. If the singular set is bounded away from the end, we have $-1
7.
Gluing construction of compact complex surfaces with trivial canonical bundle - DOI, Mamoru
We obtain a new construction of compact complex surfaces with trivial canonical bundle. In our construction we glue together two compact complex surfaces with an anticanonical divisor under suitable conditions. Then we show that the resulting compact manifold admits a complex structure with trivial canonical bundle by solving an elliptic partial differential equation. We generalize this result to cases where we have other than two components to glue together. With this generalization, we construct examples of complex tori, Kodaira surfaces and K3 surfaces. Lastly we deal with the smoothing problem of a normal crossing complex surface $X$ with at most...
8.
Finite rank product theorems for Toeplitz operators on the half-space - CHOE, Boo Rim; KOO, Hyungwoon; NAM, Kyesook
On the harmonic Bergman space of the half space in $\mbi{R}^{n}$ , we show that if the product of two or more Toeplitz operators with harmonic symbols that have certain boundary smoothness has finite rank, then one of the symbols must be identically 0. Our methods require the number of factors in the product to depend on the dimension $n$ .
9.
Asymptotic dimension of invariant subspace in tensor product representation of compact Lie group - SUZUKI, Taro; TAKAKURA, Tatsuru
We consider asymptotic behavior of the dimension of the invariant subspace in a tensor product of several irreducible representations of a compact Lie group $G$ . It is equivalent to studying the symplectic volume of the symplectic quotient for a direct product of several coadjoint orbits of $G$ . We obtain two formulas for the asymptotic dimension. The first formula takes the form of a finite sum over tuples of elements in the Weyl group of $G$ . Each term is given as a multiple integral of a certain polynomial function. The second formula is expressed as an infinite series...
10.
On the first homology of the group of equivariant Lipschitz homeomorphisms - ABE, K?jun; FUKUI, Kazuhiko; MIURA, Takeshi
We study the structure of the group of equivariant Lipschitz
homeomorphisms of a smooth $G$ -manifold $M$ which are isotopic
to the identity through equivariant Lipschitz homeomorphisms
with compact support. First we show that the group is perfect
when $M$ is a smooth free $G$ -manifold. Secondly in the case of
$\mathbf{C}^n$ with the canonical $U(n)$ -action, we show that the first homology group admits continuous moduli. Thirdly we apply the result to the case of the group $L(\mathbf{C},0)$ of Lipschitz homeomorphisms of $\mathbf{C}^n$ fixing the origin.
11.
Classification of totally real and totally geodesic submanifolds of compact 3-symmetric spaces - TOJO, Koji
It is known that each 3-symmetric space admits an invariant almost complex structure $J$ , so-called a canonical almost complex structure. By making use of simple graded Lie algebras and an affine Lie algebra, we classify half dimensional, totally real (with respect to $J$ ) and totally geodesic submanifolds of compact 3-symmetric spaces.
12.
Hodge cycles on abelian varieties associated to the complete binary trees - HAZAWA, Fumio
The structure of the ring of Hodge cycles on a certain family of abelian varieties of CM-type is investigated. This leads to an interesting combinatorial problem related to posets based on complete $p$ -ary trees. A complete solution to the problem is given for the case $p=2$ .
13.
Carleson type measures on parabolic Bergman spaces - NISHIO, Masaharu; YAMADA, Masahiro
Let $b^{p}_{\alpha}$ , $0<\alpha \le1$ , be the parabolic Bergman space, the Banach space of solutions of parabolic equations $(\partial/\partial t+(-\varDelta)^{\alpha})u=0$ on the upper half space $\mathbf{R}^{n+1}_{+}$ which have finite
$L^{p}$ norms. We study Carleson type measures
on $b^{p}_{\alpha}$ , and give a necessary and
sufficient condition for a measure $\mu$ on $\mathbf{R}^{n+1}_{+}$ to be of Carleson type
on $b^{p}_{\alpha}$ . As an application, we
characterize bounded Toeplitz operators in the
space $b^{2}_{\alpha}$ .
14.
The stable Calabi-Yau dimension of tame symmetric algebras - ERDMANN, Karin; SKOWRO?SKI, Andrzej
We determine the Calabi-Yau dimension of the stable module categories of all symmetric algebras of tame representation type over an algebraically closed field, and derive some consequences.
15.
A time-change approach to Kotani's extension of Yor's formula - HARIYA, Yuu
In [3], Kotani proved analytically that expectations for
additive functionals of Brownian motion $\{ B_t, t \ge 0 \}$ of the form
$$E_0 \bigg[ f(B_t)g \bigg( \int_0^t \varphi (B_s)ds \bigg) \bigg]$$
have the asymptotics $t^{-3/2}$ as $t\to \infty$ for some suitable non-negative functions $\varphi$ , $f$
and $g$ . This generalizes, in the asymptotic form, Yor's explicit formula [10] for exponential Brownian functionals.
¶
In the present paper, we discuss this generalization probabilistically, by using a time-change argument. We may easily see from our argument that this asymptotics $t^{-3/2}$ comes from the transition probability of 3-dimensional Bessel process.
17.
How can we escape Thomae's relations? - KRATTENTHALER, Christian; RIVOAL, Tanguy
In 1879, Thomae discussed the relations between two generic hypergeometric $_3F_2$ -series with argument 1. It is well-known since then that, in combination with the trivial ones which come from permutations of the parameters of the hypergeometric series, Thomae had found a set of 120 relations. More recently, Rhin and Viola asked the following question (in a different, but equivalent language of integrals): If there exists a linear dependence relation over $\bm{Q}$ between two convergent $_3F_2$ -series with argument 1, with integral parameters, and whose values are irrational numbers, is this relation a specialisation of one of the 120 Thomae...
18.
Projective manifolds containing special curves - B?DESCU, Lucian; BELTRAMETTI, Mauro C.
Let $Y$ be a smooth curve embedded in a complex projective manifold $X$ of dimension $n\geq 2$ with ample normal bundle $N_{Y|X}$
. For every $p\geq 0$ let $\alpha_p$ denote the natural restriction maps ${\rm Pic}(X)\to{\rm Pic}(Y(p))$ , where $Y(p)$ is the $p$ -th infinitesimal neighbourhood of $Y$ in $X$ . First one proves that for every $p\geq 1$ there is an isomorphism of abelian groups ${\rm Coker}(\alpha_p)\cong{\rm Coker}(\alpha_0)\oplus K_p(Y,X)$ , where $K_p(Y,X)$
is a quotient of the $\bm{C}$ -vector space $L_p(Y,X):=\bigoplus_{i=1}^p H^1(Y, {\bf S}^i(N_{Y|X})^*)$ by a free subgroup of $L_p(Y,X)$
of rank strictly less than the Picard number of $X$ . Then...
19.
Critical points of the symmetric functions of the eigenvalues of the Laplace operator and overdetermined problems - LAMBERTI, Pier Domenico; LANZA DE CRISTOFORIS, Massimo
We consider the Dirichlet and the Neumann eigenvalue problem for the Laplace operator on a variable nonsmooth domain, and we prove that the elementary symmetric functions of the eigenvalues splitting from a given eigenvalue upon domain deformation have a critical point at a domain with the shape of a ball. Correspondingly, we formulate overdetermined boundary value problems of the type of the Schiffer conjecture.
20.
Martin boundary points of a John domain and unions of convex sets - AIKAWA, Hiroaki; HIRATA, Kentaro; LUNDH, Torbjörn
We show that a John domain has finitely many minimal Martin boundary points at each Euclidean boundary point. The number of minimal Martin boundary points is estimated in terms of the John constant. In particular, if the John constant is bigger than $\sqrt3/2$
, then there are at most two minimal Martin boundary points at each Euclidean boundary point. For a class of John domains represented as the union of convex sets we give a sufficient condition for the Martin boundary and the Euclidean boundary to coincide.
1.
