Mathematical Sciences: Problems in Modern Analysis

恩弗洛教授和罗蒙诺索夫教授将探索一些领域 分析的问题包括：（1）数论中的问题， 数论和的界，（2）Banach空间中的非线性问题 空间，包括同胚和 Banach空间的同构;（3）不变子空间 问题. 恩弗洛教授和罗蒙诺索夫教授将研究的问题 是非常多样化的。 也许最重要的是他们的关节 不变子空间问题的解决方案。 有限维 空间中，每个线性算子（矩阵）都有一个特征向量，因此 该向量的倍数形成不变子空间。 这不是 在无限维中不再成立，但在重要维中仍然成立。 特殊情况。 主要研究人员将研究 在某种程度上，某些类型的算子具有非平凡不变量 特殊但重要的无限维空间中的子空间。

Professors Enflo and Lomonosov will explore a number of areas of analysis including: (1) problems in number theory involving bounds on number theoretic sums, (2) non-linear problems in Banach spaces including the relationship between homeomorphisms and isomorphisms of Banach spaces, and (3) the invariant subspace problem. The problems which Professors Enflo and Lomonosov will study are extremely diverse. Perhaps the most important is their joint project on the invariant subspace problem. In a finite dimensional space, every linear operator (matrix) has an eigenvector and thus multiples of this vector form an invariant subspace. This is no longer true in infinite dimensions but remains true in important special cases. The principal investigators will study to what extent certain classes of operators have nontrivial invariant subspaces in special but important infinite dimensional spaces.