Mathematische Nachrichten最新文献

This study deals with the Ulam stability of nonautonomous linear differential systems without assuming the condition that they admit an exponential dichotomy. In particular, the best (minimal) Ulam constants for two-dimensional nonautonomous linear differential systems with generalized Jordan normal forms are derived. The obtained results are applicable not only to systems with solutions that exist globally on $��(�-�\infty �,�\infty �)�$, but also to systems with solutions that blow up in finite time. New results are included even for constant coefficients. A wealth of examples are presented, and approximations of node, saddle, and focus are proposed. In addition, this is the first study to derive the best Ulam constants for nonautonomous systems other than periodic systems.

We consider the following fractional problem involving slightly subcritical non-power nonlinearity,

This paper deals with regularity properties for variational integrals with the splitting structure of the form

We consider the action of the d'Alembertian on functions on the pseudo-Riemannian three-dimensional anti-de Sitter space. We determine the resonances of this operator. With each resonance one can associate a residue representation. We give an explicit description of these representations via Langlands parameters.

Let $��1�\le �p�<�\infty �$ and $��0�<�q�,�r�<�\infty �$. We characterize the validity of the inequality for the composition of the Hardy operator,

In this paper, we study Rubio de Francia extrapolation theorems in the framework of the variable grand Lebesgue spaces with $�B_{�p�(�·�)�}$ weights. As an application of the extrapolation theorems, we prove the boundedness of the Hardy averaging operator and the fractional Riemann Liouville transform for nonnegative and nonincreasing measurable functions. Some structural properties of the weighted grand Lebesgue spaces with variable exponent are also investigated.

In this work, we give three kinds of criteria for weak sets in Orlicz–Bochner sequence spaces $��l_{�\left(�\Phi �\right)�}��\left(�X�\right)��$ without constraints, conditions posited in each criterion are necessary and sufficient. As an application, we give criteria for weak sets in Orlicz sequence spaces. Well-known conclusions are exhibited once more, such as Schur's theorem, Banach–Alaoglu's theorem, and the boundedly compact principle of finite dimension space. The results obtained show that the weak compactness may not be extrapolated straightforwardly from $�X$ to $��l_{�\left(�\Phi �\right)�}��\left(�X�\right)��$, for example, $��l_{\infty }��\left(�X�\right)��$.

In this paper, we provide several techniques to explicitly calculate fractional powers of $��2�\times �2�$ operator matrices

Let $�\xi$ be an analytic bracket-generating distribution. We show that the subspace of germs that are singular (in the sense of control theory) has infinite codimension within the space of germs of smooth curves tangent to $�\xi$. We formalize this as an asymptotic statement about finite jets of tangent curves. This solves, in the analytic setting, a conjecture of Eliashberg and Mishachev regarding an earlier claim by Gromov about the microflexibility of the tangency condition.

From these statements it follows, by an argument due to Gromov, that the $�h$-principle holds for maps and immersions transverse to $�\xi$.