Topological Algebras with Finitely-Generated Bases.
Structure spaces for rings of continuous functions with applications to realcompactifications
Let X be a completely regular space and let A(X) be a ring of continuous real-valued functions on X which is closed under local bounded inversion. We show that the structure space of A(X) is homeomorphic to a quotient of the Stone-Čech compactification of X. We use this result to show that any realcompactification of X is homeomorphic to a subspace of the structure space of some ring of continuous functions A(X).
A local algebra structure for of the polydisc
A multiplier theorem for Fourier series in several variables
We define a new type of multiplier operators on , where is the N-dimensional torus, and use tangent sequences from probability theory to prove that the operator norms of these multipliers are independent of the dimension N. Our construction is motivated by the conjugate function operator on , to which the theorem applies as a particular example.
Correspondences between ideals and -filters for rings of continuous functions between and
Let be a completely regular topological space. Let be a ring of continuous functions between and , that is, . In [9], a correspondence between ideals of and -filters on is defined. Here we show that extends the well-known correspondence for to all rings . We define a new correspondence and show that it extends the well-known correspondence for to all rings . We give a formula that relates the two correspondences. We use properties of and to characterize and among...
Irregular amalgams.
A characterization of the algebra of holomorphic functions on simply connected domain.
Page 1