Various sequences that possess explicit analytic expressions can be analysed asymptotically through integral representations due to Lindelöf, which belong to an attractive but largely forgotten chapter of complex analysis. One of the outcomes of such analyses concerns the non-existence of linear recurrences with polynomial coefficients annihilating these sequences, and, accordingly, the non-exi...

Given a class $${{\mathcal {P}}}$$ of Banach spaces, locally convex space (LCS) E is called multi- if can be isomorphically embedded into product spaces that belong to . We investigate the question whether free L(X) strongly nuclear, Schwartz, multi-Hilbert or multi-reflexive. If X Tychonoff containing an infinite compact subset then, as it follows from results Außenhofer (Topol Appl 134:90–102...

We study three problems which involve the nature of subspaces of the Sorgenfrey Line S. It is shown that no integer power of an uncountable subspace of S can be embedded in a smaller power of S. We review the known results about the existence of uncountable X ⊆ S where X is Lindelöf. These results about Lindelöf powers are quite set-theoretic. A descriptive characterization is given of those su...

We apply and develop an idea of E. van Douwen used to define D-spaces. Given a topological property P , the class P∗ dual to P (with respect to neighbourhood assignments) consists of spaces X such that for any neighbourhood assignment {Ox : x ∈X} there is Y ⊂X with Y ∈P and {Ox : x ∈ Y } =X. We prove that the classes of compact, countably compact and pseudocompact are self-dual with respect to ...