The object is to unify and complement some recent theorems of Hewitt and Ritter on the integrability of Fourier transforms, but the underlying theme is the ancient one that Plancherel's theorem is the “only” integrability constraint on Fourier transforms. The distinguishing feature of the results is that we restrict attention to positive measures (or functions) which satisfy an ergodic condition and whose transforms are positive. (In fact we employ sums of discrete random variables, a technique which seems to have been largely ignored in context.) The general setting is that of locally compact abelian groups but we are chiefly interested in the line or the circle, and it appears that the theorems are new for these classical groups.

Totally umbilical submanifolds of dimension greater than four in quaternion-space-forms are completely classified.

Complemented congruences in the classes of pseudocomplemented semilattices, p-algebras and double p-algebras are described. The descriptions are applied to give intrinsic characterizations of those algebras in the aforementioned classes whose congruence lattice is a Boolean algebra.

Some fixed point theorems are obtained for weekly inward mappings which extend or generalize those results by K. Fan, B. Halpern or S. Reich. Various formulations of inward and outward concepts are also briefly discussed.

Let Un be the unit polydisc in Cn and let Tn be its distinguished boundary. It is shown that a function f ∈ H∞(Un) is inner if and only if ∣f(Φ)∣ = 1 for all Φ in the maximal ideal space of L∞(Tn). This generalizes a result of Csordas.

An elementary and self-contained account of analytic Jordan decomposition of matrix-valued analytic functions is given. An integral representation for their eigenvalues is obtained. This leads to estimates of the differences in eigenvalues and the number of points of degeneracy.

Ore (1942) studied the automorphisms of finite monomial groups and Holmes (1956, pp. 23–93) has given the form of the automorphisms of the restricted monomial groups in the infinite case. The automorphism group of a standard wreath product has been studied by Houghton (1962) and Segal (1973, Chapter 4). Monomial groups and standard wreath products are both special cases of permutational wreath product. Here we investigate the automorphisms of the permutational wreath product and consider to what extent the results holding in the special cases remain true for the general construction. Our results extend those of Bunt (1968).

This paper is devoted to a study of pseudocomplements in groupoids. A characterization of an intraregular groupoid is obtained in terms of prime ideals. It is proved that the set of dense elements of an intraregular groupoid S with 0 is the intersection of all the maximal filters of S and that the set of normal elements of an intraregular groupoid closed for pseudocomplements forms a Boolean algebra under natural operations. It is shown that the pseudocomplement of an ideal of an intraregular groupoid with 0 is the intersection of all the minimal prime ideas not containing it.

A generalized version of the Knaster-Kuratowski-Mazurkiewicz theorem is obtained and used to generalize Ky Fan's minimax principle. This result is applied to a variational inequality.

Let T be a continuous t-norm (a suitable binary operation on[0, 1]) and Δ + the space of distribution functions which are concertratede on [0,∞. theτT product of any F, G in Δ+ is defined at any real x by , and the pair (Δ+, τT) forms a semigroup. Thus, given a sequence {Fi} in Δ+, the n-fold product τT(F1 … Fn) is well-defined for each n. Moreover, that resulting sequence {τT(F1, …, Fn)} is pointwise non-increasing and hence has a weak limit. This paper establishes a convergence theorem which yields a representation for this weak limit. In addition, we prove the Zero-One law that, for Archimedean t-norms, the weak limit is either identically zero or has supremum 1.

Several pairwise concepts have been studied for bitopological spaces. In this note an attempt has been made to see how much ‘bitopological’ these pairwise concepts are. For example pairwise T1 is purely a topological concept whereas pairwise normality is very much ‘bitopological’. Several questions pertaining to this theme are dealt with.

It is shown that a Tychonoff space X is pseudocompact if and only if for every metrizable space Y, all uniformities on Y induce the same topology on the space of continuous functions from X into Y. Also for certain pairs of spaces X and Y, a necessary and sufficient condition is established in order that all uniformities on Y induce the same topology on the space of continuous functions from X into Y.