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Ordered reproducing Hilbert spaces over ℂ2
Springer Science and Business Media LLC - Tập 24 - Trang 503-510 - 2008
In this paper, we study the relation between the ordered reproducing Hilbert space and its reproducing kernel. A complete description of a similar and unitary equivalence of two quasi-invariant subspaces generated by polynomials with leading terms is given.
The Neumann Problem for Parabolic Hessian Quotient Equations
Springer Science and Business Media LLC - Tập 37 - Trang 1313-1348 - 2021
In this paper, we consider the Neumann problem for parabolic Hessian quotient equations. We show that the k-admissible solution of the parabolic Hessian quotient equation exists for all time and converges to the smooth solution of elliptic Hessian quotient equations. Also solutions of the classical Neumann problem converge to a translating solution.
Small prime solutions of a pair of linear equations in five prime variables
Springer Science and Business Media LLC - - 2010
A remark on the generalized second order Toda system
Springer Science and Business Media LLC - Tập 29 - Trang 1691-1702 - 2013
In this paper, we establish a priori estimates to the generalized second order Toda system
$$\left\{ \begin{gathered}
- \Delta u_1 (x) = 2R_1 (x)e^{u_1 } - R_2 e^{u_2 } , \hfill \\
- \Delta u_2 (x) = - R_1 (x)e^{u_1 } + 2R_2 e^{u_2 } \hfill \\
\end{gathered} \right.$$
in ℝ2, and discuss the c......
Representation of numbers by binary quadratic forms
Springer Science and Business Media LLC - Tập 3 - Trang 58-65 - 1987
On a Problem of D. H. Lehmer
Springer Science and Business Media LLC - Tập 22 - Trang 61-68 - 2005
The main purpose of this paper is to use the Fourier expansion for character sums and
the mean value theorem of Dirichlet L–functions to study the asymptotic property of the difference
between a D. H. Lehmer number and its inverse modulo p (an odd prime). A interesting mean square
value formula is also given.
Dyadic bivariate wavelet multipliers in L 2(ℝ2)
Springer Science and Business Media LLC - Tập 27 - Trang 1489-1500 - 2011
The single 2 dilation wavelet multipliers in one-dimensional case and single A-dilation (where A is any expansive matrix with integer entries and |detA| = 2) wavelet multipliers in twodimensional case were completely characterized by Wutam Consortium (1998) and Li Z., et al. (2010). But there exist no results on multivariate wavelet multipliers corresponding to integer expansive dilation matrix wi......
A fibration of categories overH B
Springer Science and Business Media LLC - Tập 13 - Trang 553-562 - 1997
K. A. Hardie and K. H. Kamps investigated the track homotopy categoryH
B over a fixed spaceB ([5]). This paper extendsH
B to the track homotopy categoryH
b over a fixed mapb:
$$B \to \bar B$$
, such that there exists a split fibration of categoriesL:H
......
Global Existence of Solutions for the Kawahara Equation in Sobolev Spaces of Negative Indices
Springer Science and Business Media LLC - Tập 23 - Trang 1435-1446 - 2007
We first prove that the Cauchy problem of the Kawahara equation,
$$
\partial _{t} u + u\partial _{x} u + \beta \partial ^{3}_{x} u + \gamma \partial ^{5}_{x} u = 0
$$
, is locally solvable if the initial data belong to H
r
(R) and
......
A concentration behavior for semilinear elliptic systems with indefinite weight
Springer Science and Business Media LLC - Tập 30 - Trang 2014-2026 - 2014
Consider the Schrödinger system
$\left\{ \begin{gathered}
- \Delta u + V_{1,n} u = \alpha Q_n (x)|u|^{\alpha - 2} u|v|^\beta , \hfill \\
- \Delta v + V_{2,n} v = \beta Q_n (x)|u|^\alpha |v|^{\beta - 2} v, \hfill \\
u,v \in H_0^1 (\Omega ), \hfill \\
\end{gathered} \right.$
where Ω ⊂ ℝ
......
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