Acta Mathematica Sinica-English Series最新文献

Pseudo-differential operators (PDO) (Q(x,{{cal L}_{a,x}})) and ({cal Q}(x,{{cal L}_{a,x}})) involving the index Whittaker transform are defined. Estimates for these operators in Hilbert space L ^a₂ (ℝ₊;m_a(x)dx) are obtained. A symbol class Ω is introduced. Later product and commutators for the PDO are investigated and their boundedness results are discussed.

The eccentricity matrix of a graph is obtained from the distance matrix by keeping the entries that are largest in their row or column, and replacing the remaining entries by zero. This matrix can be interpreted as an opposite to the adjacency matrix, which is on the contrary obtained from the distance matrix by keeping only the entries equal to 1. In the paper, we determine graphs having the second largest eigenvalue of eccentricity matrix less than 1.

In this paper, pseudo-differential operators with homogeneous symbol classes associated with the Weinstein transform are introduced. The boundedness of pseudo-differential operators and commutator between two pseudo-differential operators on ℌ ^r_α,2 are proven with the help of the Weinstein transform technique.

In this paper, we describe the minimal reducing subspaces of Toeplitz operators induced by non-analytic monomials on the weighted Bergman spaces and Dirichlet spaces over the unit ball ({mathbb{B}_2}). It is proved that each minimal reducing subspace M is finite dimensional, and if dim M ≥ 3, then M is induced by a monomial. Furthermore, the structure of commutant algebra (nu ({T_{overline w {N_z}N}}): = {{ M_{{w^N}}^ * {M_{{z^N}}},M_{{z^N}}^ * {M_{{w^N}}}} ^prime }) is determined by N and the two dimensional minimal reducing subspaces of ({T_{overline w {N_z}N}}). We also give some interesting examples.

In this paper, we prove that for each positive k ≡ 1 mod m there exists a P-symmetric kmτ-periodic solution x_k for asymptotically linear mτ-periodic Hamiltonian systems, which are nonautonomous and endowed with a P-symmetry. If the P-symmetric Hamiltonian function is semi-positive, one can prove, under a new iteration inequality of the Maslov-type P-index, that ({x_{{k_1}}}) and ({x_{{k_2}}}) are geometrically distinct for k₁/k₂ ≥ (2n + 1)m + 1; and ({x_{{k_1}}}), ({x_{{k_2}}}) are geometrically distinct for k₁/k₂ ≥ m + 1 provided ({x_{{k_1}}}) is non-degenerate.

Let G be a special linear group over the real, the complex or the quaternion, or a special unitary group. In this note, we determine all special unipotent representations of G in the sense of Arthur and Barbasch–Vogan, and show in particular that all of them are unitarizable.

This paper is concerned with the problem of stability discrimination of limit cycles for piecewise smooth systems. We first establish the Poincaré map near a periodic orbit, and deduce the first order derivative of the map for general piecewise smooth systems on the plane. Then, we obtain a sufficient condition for determining the stability of limit cycles for these systems.

We study the transfer between small special unipotent representations for all equal rank real forms of type E₆ and E₇. As a consequence, one can verify these modules are unitarity using the results of Wallach and Zhu. Moreover, the K-spectra of these modules can be obtained explicitly.

The first passage time has many applications in fields like finance, econometrics, statistics, and biology. However, explicit formulas for the first passage density have only been obtained for a few cases. This paper derives an explicit formula for the first passage density of Brownian motion with two-sided piecewise continuous boundaries which may have some points of discontinuity. Approximations are used to obtain a simplified formula for estimating the first passage density. Moreover, the results are also generalized to the case of two-sided general nonlinear boundaries. Simulations can be easily carried out with Monte Carlo method and it is demonstrated for several typical two-sided boundaries that the proposed approximation method offers a highly accurate approximation of first passage density.

In this paper we consider the theta correspondence over a non-Archimedean local field. Using the homological method and the theory of derivatives, we show that under a mild condition the big theta lift is irreducible.