The Structure of Inner Multipliers on Spaces with Complete Nevanlinna Pick Kernels

We establish some multivariate generalizations of the Beurling-Lax-Halmos theorem.Comment: 21 page

Zeros of Functions with Finite Dirichlet Integral

In this paper, we refine a result of Nagel, Rudin, and Shapiro (1982) concerning the zeros of holomorphic functions on the unit disk with finite Dirichlet integral

Ruderal vascular plants on a waste ground in the island of Dånö, Åland Islands, SW Finland

The Åland Islands, SW Finland, are known for luxuriant vegetation with numerous calciphilic vascular plants, but ruderal plants are rather few compared to the adjoining regions of Finland and Sweden. However, new ruderal plants are occasionally found in Åland. We came across a waste ground in the island of Dånö, municipality of Geta, on which several non-familiar vascular plants grew. The waste ground has been used for dumping flower shop garbage and thus some unfamiliar plants have been dumped there. The following species have not been found previously as ruderal plants in the Åland Islands: Allium sativum, Cucumis melo, Dipsacus fullonum, Hedera helix, Inula helenium and Lactuca serriola. Several other more or less rare ruderals were also found on the waste ground: Bromus secalinus, Conyza canadensis, Holcus lanatus, Lepidium densiflorum subsp. neglectum and Senecio jacobaea. Three garden shrubs, Rosa spinosissima, Symphoricarpos albus var. laevigatus and Salix viminalis grew together with more common garden ruderals, such as Digitalis purpurea, Malva moschata and Saponaria officinalis. A total of 137 vascular plant taxa, most of them common in the Åland Islands, were observed growing on the waste ground

Linear graph transformations on spaces of analytic functions

Let H be a Hilbert space of analytic functions with multiplier algebra M(H), and let M = {(f, T(1)f, ... ,T(n-1)f) : f is an element of D} be an invariant graph subspace for M(H)((n)). Here n >= 2, D subset of H is a vector-subspace, T-i : D -> H are linear transformations that commute with each multiplication operator M-phi is an element of M(H), and M is closed in H-(n). In this paper we investigate the existence of non-trivial common invariant subspaces of operator algebras of the type A(M) = {A is an element of B(H) : AD subset of D : AT(i)f = T(i)Af for all f is an element of D}. In particular, for the Bergman space L-0,(2) we exhibit examples of invariant graph subspaces of fiber dimension 2 such that A(M) does not have any nontrivial invariant subspaces that are defined by linear relations of the graph transformations for M. (C) 2015 Elsevier Inc. All rights reserved

Epilobium hirsutum in the Åland Islands, SW Finland

Epilobium hirsutum L. is an introduced species in Finland with the first reliable findings made in the late 19th century. The number of new findings accumulated slowly during the period 1900–1929. From the 1930’s onwards, the number of findings grew rapidly and E. hirsutum has been found in 153 grid squares of 10 km × 10 km size in the southern part of Finland until 2012. The first information of the species in the Åland Islands is a note in the literature from 1821 and the first collected specimen in the Åland Islands is from the municipality of Sund in 1873. However, both these are doubtful as they were not noticed in Finnish vascular plant floras later on. The first reliable finding is from 1973 and thereafter the localities with E. hirsutum increased with four more during the 1970’s, eight new during the 1980’s, fourteen new during the 1990’s and 35 new localities during the period 2000–2013. It thrives chiefly in man-made habitats in the cultural landscape and the most common habitats in the Åland Islands seem to be roadsides and road ditches. Although E. hirsutum has expanded during the last fifty years in Åland, it is not common yet and it has not been found in most of the eastern archipelago area. As an immigrant in our flora, E. hirsutum is now well established in the Åland Islands and it will probably be more common in the future. However, it seems that it is not a harmful invasive weed in Åland

A new record of Arctic Bramble, Rubus arcticus, in the Åland Islands, SW Finland

The Arctic Bramble, Rubus arcticus L., was found in Gottby in the municipality of Jomala, the Åland Islands, SWFinland, in June 2009. It was both flowering and fruiting, although rather sparingly. This boreal species has not been observed in the Åland Islands since 1950. The total distribution of the species is outlined.An account is given of the previous six observations of R. arcticus in Åland. The dispersal of the seeds (endocarps with seeds) of R. arcticus is treated