Showing papers on "Uniform boundedness published in 1974"
TL;DR: In this paper, the authors introduce a formulation for two-dimensional Pade approximant theory, and prove a theorem on convergence under the stringent assumption of uniform boundedness, and discuss some general problems connected with rational functions in several variable theory.
Abstract: The author introduces a formulation for two-dimensional Pade approximant theory, and proves a theorem on convergence under the stringent assumption of uniform boundedness. Finally he discusses some general problems connected with rational functions in several variable theory.
36 citations
13 citations
TL;DR: In this paper, the sequences {λn} and {αn} of complex numbers satisfy the conditions: 1) sup ¦Im λn¦=h<∞; 2) the number of points in the rectangle ¦t−Re z¦-1, ¦ im z©≤h is uniformly bounded with respect to t e (−∞, ∞); 3) αn} elP for some p <∞.
Abstract: Let the sequences {λn} and {αn} of complex numbers satisfy the conditions: 1) sup ¦Im λn¦=h<∞; 2) the number of points λn in the rectangle ¦t−Re z¦-1, ¦Im z¦≤h is uniformly bounded with respect to t e (−∞, ∞); 3) {αn} elP for some p<∞ Then the systems {exp (iλnx)} and {exp(ix(λn+αn))} are simultaneously complete or noncomplete (minimal or nonminimal) in L2(−a, a) (a<∞)
11 citations
01 Jan 1974
TL;DR: For every separable Banach space X a biorthogonal sequence (x,x ) is constructed such that linear combinations of the xl s are n n 4~" n dense in X, for every x in X if x (x) 0 for all n then x = 0 and CJ, n n 11 11 11 2) Linear subspaces of which admit an orthonormal basis consisting of uniformly bounded functions are characteri-zed.
Abstract: 1) Tn every separable Banach space X a biorthogonal sequence (x ,x ) is constructed such that linear combinations of the xl s are n n 4~ "" n dense in X, for every x in X if x (x) 0 for all n then x = 0 and CJ , n n 11 11 2) Linear subspacps of which admit an orthonormal basis consisting of uniformly bounded functions are characteri-zed.
6 citations
01 Jan 1974
3 citations
3 citations
1 citations
01 Mar 1974
TL;DR: In this paper, the class of almost periodic functions and almost automorphic functions has the bounded difference property, where the range of functions is relatively compact in the dual of a Hausdorff topological group G to a Banach space E such that k 0 f is in A(G, C) for each k in G.
Abstract: Let A(G, E) denote the set of functions f from a Hausdorff topological group G to a Banach space E such that the range of f is relatively compact in E and k 0 f is in A(G, C) for each k in the dual of E, where A(G, C) is a translation-invariant C* algebra of bounded, continuous, complexvalued functions on G with respect to the supreinum norm and complex conjugation. A(G, E) has the bounded difference property if whenever F: G -_. E is a bounded function such that A1F(x) = F(tx) F(x) is in A(G, E) for each t in G, then F is also an element of A(G, E). A condition on A(G, C) and a condition on E are given under which A(G, E) has the bounded difference property. The condition on A(G, C) is satisfied by both the class of almost periodic functions and the class of almost automorphic functions.