Related papers: Contractive projections in nonatomic function spac…
We construct a complete locally convex topological vector space $X$ of countable algebraic dimension and a continuous linear operator $T:X\to X$ such that $T$ has no non-trivial closed invariant subspaces.
The structure of exponential subspaces of finitely generated shift-invariant spaces is well understood and the role of such subspaces for the approximation power of refinable function vectors and related multi-wavelets is well studied. In…
We prove that it is consistent with large values of the continuum that there are no S-spaces. We also show that we can also have that compact separable spaces of countable tightness have cardinality at most the continuum.
We prove that there do not exist odd-dimensional stable compact minimal immersions in the product of two complex projective spaces. We also prove that the only stable compact minimal immersions in the product of a quaternionic projective…
Consider a finite collection $\{T_1, \ldots, T_J\}$ of differential operators with constant coefficients on $\mathbb{T}^2$ and the space of smooth functions generated by this collection, namely, the space of functions $f$ such that $T_j f…
We show that an equivariantly embedded Hermitian symmetric space in a projective space, which contains neither a projective space nor a hyperquadric as a component, is characterized by their fundamental forms as a local submanifold of the…
Non-dicritical codimension one foliations on projective spaces of dimension four or higher always have an invariant algebraic hypersurface. The proof relies on a strengthening of a result by Rossi on the algebraization/continuation of…
A contractive condition is addressed for extended 2-cyclic self-mappings on the union of a finite number of subsets of a metric space which are allowed to have a finite number of successive images in the same subsets of its domain. It is…
We show that there are no non-trivial closed subspaces of $L_2(\mathbb{R}^n)$ that are invariant under invertible affine transformations. We apply this result to neural networks showing that any nonzero $L_2(\mathbb{R})$ function is an…
Motivated by Gray's work on tube formulae for complex submanifolds of complex projective space equipped with the Fubini-Study metric, Riemannian foliations of projective space are studied. We prove that there are no complex Riemannian…
We consider a space of infinitely smooth functions on an unbounded closed convex set in ${\mathbb R}^n$. It is shown that each function of this space can be extended to an entire function in ${\mathbb C}^n$ satisfying some prescribed growth…
We prove that for an isometric representation of some groups on certain Banach spaces, the complement of the subspace of invariant vectors is 1-complemented.
Working over the field of order 2 we consider those complete caps (maximal sets of points with no three collinear) which are disjoint from some codimension 2 subspace of projective space. We derive restrictive conditions which such a cap…
Motivated by the smallness of the cosmological constant we investigate whether it is possible to have vanishing one-loop heterotic string partition functions for six-dimensional non-supersymmetric toroidal orbifolds. A straightforward way…
We introduce a new operation, copolar addition, on unbounded convex subsets of the positive orthant of real euclidean space and establish convexity of the covolumes of the corresponding convex combinations. The proof is based on a technique…
We prove that every reduced Stein space admits a holomorphic function without critical points. Furthermore, any closed discrete subset of such a space is the critical locus of a holomorphic function. We also show that for every complex…
From the Lytchak's result for polar foliations on an irreducible simply connected symmetric space $G/K$ of compact type and rank greater than one, we can derive that there exists no equifocal submanifold with non-flat section whose…
We provide a direct proof of a result regarding the asymptotic behavior of alternating nearest point projections onto two closed and convex sets in a Hilbert space. Our arguments are based on nonexpansive mapping theory.
New rigidity results for complete non-compact spacelike submanifolds of arbitrary codimension in plane fronted waves are obtained. Under appropriate assumptions, we prove that a complete spacelike submanifold in these spacetimes is…
The main aim of this work is to show, in the absence of the Axiom of Choice, fundamental results on $\mathbf{E}$-compact extensions of $\mathbf{E}$-completely regular spaces, in particular, on Hewitt realcompactifications and Banaschewski…