We apply this series to prove that for any group G acting on a tree in such a way that the stabilizer of a vertex is a compact subgroup of G the Fourier algebra A(G) admits an approximate unit bounded in the multiplier norm on A(G).
Theorem 4 Given a function χ ( s, t ) ∈ B V [ 0, 1 ] × [ 0, 1 ], a bounded variation in the unit square, the corresponding double E-J Hausdorff transformation ( t m n ), of a sequence ( s m n ), may be defined by t m n = ∑ i = 0 m ∑ j = 0 n ( m + α m − i ) ( n + β n − j ) s i j ∫ 0 1 ∫ 0 1 s i + α ( 1 − s ) m − i t j + β ( 1 − t ) n − j d χ ( s, t ).
We study the approximation of a bounded matrix-valued function G on the unit circle by functions Q bounded and analytic in the unit disc.
A major open problem asks about the (Grothendieck) approximation property for the space H∞:="H∞ D) of bounded holomorphic functions in the unit disk D⊂C.
In this paper, we study the Rudin orthogonality problem on the Bergman space, which is to characterize those functions bounded analytic on the unit disk whose powers form an orthogonal set in the Bergman space of the unit disk.
The paper deals with the problem of ideals of H∞: describe increasing functions φ⩾0 such that for all bounded analytic functions f1,…,fn,fn,τ in the unit disc D the condition∣∣τ z)∣∣⩽φ((∑∣∣fk z)∣∣2)1/2)∀z∈D implies that τ belong to the ideal generated by f1,…,fn,fn, i.e. that there exist bounded analytic functions g1,g2,…,gn such that ∑k= 1nfkgk="τ.
Simeone bounded in beaming.
We study the completion problem to an invertible operator-valued function for the class of bounded holomorphic functions on the unit disk D⊂S with relatively compact images in the space of bounded linear operators between complex Banach spaces.
In her doctoral thesis, Chang worked on problems in classical analysis, in particular the study of boundary behavior of bounded analytic functions on the unit disc.
