Related papers: A note on holomorphic extensions
We provide and discuss complex analytic methods for overcoming the formal character of formal deformation quantization. This is a necessity for returning to physically meaningful statements, and accounts for the fact that the formal…
We show that a large class of formal groups can be realised functorially by even periodic ring spectra. The main advance is in the construction of morphisms, not of objects.
We derive finite rational formulas for the traces of cycle integrals of certain meromorphic modular forms. Moreover, we prove the modularity of a completion of the generating function of such traces. The theoretical framework for these…
It is known that a real analytic CR function f on a real analytic, generic submanifold M in C^N can be holomorphically extended. A stronger result on a finite type, real analytic, generic submanifold M is found in which we assume f a…
It is believed that Dirichlet series with a functional equation and Euler product of a particular form are associated to holomorphic newforms on a Hecke congruence group. We perform computer algebra experiments which find that in certain…
Hypergeometric functions and their generalizations play an important r\^{o}les in diverse applications. Many authors have been established generalizations of hypergeometric functions by a number ways. In this paper, we aim at establishing…
We study groups of formal diffeomorphisms in several complex variables. For abelian, metabelian or nilpotent groups we investigate the existence of suitable formal vector fields and closed differential forms which exhibit an invariance…
We generalize the Oka extension theorem, and obtain bounds on the norm of the extension, by using operator theory.
The decompositions of an element of a finite von Neumann algebra into the sum of a normal operator plus an s.o.t.-quasinilpotent operator, obtained using the Haagerup--Schultz hyperinvariant projections, behave well with respect to…
We present a comprehensive survey on removability of compact plane sets with respect to various classes of holomorphic functions. We also discuss some applications and several open questions, some of which are new.
In this note, we establish some new results on some special types of function algebras and also give new proofs to some existing ones
In this paper, we obtain some factorization results on formal power series over principle ideal domains with sharp bounds on number of irreducible factors. These factorization results correspondingly lead to irreducibility criteria for…
In this paper, as an application of Zalcman's lemma in $\mathbb{C}^n$, we give a sufficient condition for normality of holomorphic functions of several complex variables, which generalizes previous known one-dimensional criterion of A.J.…
We announce a scale of Blaschke-type conditions for subsequences of zeros of holomorphic functions on arbitrary domains in the extended complex plane.
In this paper we will give an explicit construction of the geometric model for a prescribed extension of a function field in several variables over a number field. As a by-product, we will also prove the existence of quasi-galois closed…
The classical Riordan groups associated to a given commutative ring are groups of infinite matrices (called Riordan arrays) associated to pairs of formal power series in one variable. The Fundamental Theorem of Riordan Arrays relates matrix…
We give a polymorphic account of the relational algebra. We introduce a formalism of ``type formulas'' specifically tuned for relational algebra expressions, and present an algorithm that computes the ``principal'' type for a given…
This is an anthology of series involving rational, factorial, and power functions expressed in terms of special functions. New finite expansions involving quotient functions expressed in terms of the Hurwitz-Lerch zeta function are given.…
We study the existence of formal Taylor expansions for functions defined on fields of generalised series. We prove a general result for the existence and convergence of those expansions for fields equipped with a derivation and an…
We generalize Rado's extension theorem to complex spaces.