Analytic continuation of holomorphic functions with values in a locally convex space

Numerical analytic continuation of holomorphic functions in Cn

Singular values of convex functions of matrices

‎Let $A_{i},B_{i},X_{i},i=1,dots,m,$ be $n$-by-$n$ matrices such that $‎sum_{i=1}^{m}leftvert A_{i}rightvert ^{2}$ and $‎sum_{i=1}^{m}leftvert B_{i}rightvert ^{2}$  are nonzero matrices and each $X_{i}$ is‎ ‎positive semidefinite‎. ‎It is shown that if $f$ is a nonnegative increasing ‎convex function on $left[ 0,infty right) $ satisfying $fleft( 0right)‎ ‎=0 $‎, ‎then  $$‎2s_{j}left( fleft( fra...

Analytic Functions That Take Values in a Convex Region

that are convergent in E, the unit circle \z\ <1, and for which 9î/(z) >0 in E. We let í(l, FT) denote the family of such functions. In this notation 1 =/(0), and H denotes the half-plane 9fat>>0, in which the values of f(z) are required to lie for z in E. Herglotz [3] and later others (see Nevanlinna [6, p. 185]) proved that if/(z) £ï(l, H) then it has a representation as a Stieltjes integral,...

The Distribution of Values of Analytic Functions on Convex Sets

Proceeding the study of local properties of analytic functions started in [Br] we prove new dimensionless inequalities for such functions in terms of their Chebyshev degree. As a consequence we obtain the reverse Hölder inequalities for analytic functions with absolute (i.e., independent of dimension) constants. For polynomials such inequalities were recently proved by Bobkov who sharpened and ...

Strongly almost ideal convergent sequences in a locally convex space defined by Musielak-Orlicz function

In this article, we introduce a new class of ideal convergent sequence spaces using an infinite matrix, Musielak-Orlicz function and a new generalized difference matrix in locally convex spaces. We investigate some linear topological structures and algebraic properties of these spaces. We also give some relations related to these sequence spaces.