where / i s the boundary function for jpand da is Lebesgue measure on the sphere. When m = 1, (1) easily transforms into the Cauchy integral formula. In dimension m9 the formula extends to be defined on all / in L , always yielding holomorphic functions. If we identify holomorphic functions with their boundary values, the extended operator can be regarded as the orthogonal projection from L to ...

We develop complex function theory within certain algebras of holomorphic functions on coverings of Stein manifolds. This, in particular, includes the topics of holomorphic extension from complex submanifolds, corona type theorems, properties of divisors, holomorphic analogs of the Peter-Weyl approximation theorem, Hartogs type theorems, characterization of uniqueness sets. Our model examples c...

We establish basic results of complex function theory within certain algebras of holomorphic functions on coverings of Stein manifolds (such as algebras of Bohr’s holomorphic almost periodic functions on tube domains or algebras of all fibrewise bounded holomorphic functions arising, e.g., in the corona problem for H∞). In particular, in this context we obtain results on holomorphic extension f...

We develop complex function theory within certain algebras of holomorphic functions on coverings of Stein manifolds. This, in particular, includes the results on holomorphic extension from complex submanifolds, corona type theorems, properties of divisors, holomorphic analogs of the Peter-Weyl approximation theorem, Hartogs type theorems, characterization of uniqueness sets. The model examples ...

We prove that functions of intrinsic-mode type (a classical models for signals) behave essentially like holomorphic functions: adding a pure carrier frequency eint ensures that the anti-holomorphic part is much smaller than the holomorphic part ‖P−(f)‖L2 ‖P+(f)‖L2 . This enables us to use techniques from complex analysis, in particular the unwinding series. We study its stability and convergenc...

We use discrete holomorphic polynomials to prove that, given a refining sequence of critical maps of a Riemann surface, any holomorphic function can be approximated by a converging sequence of discrete holomorphic functions.

This is a survey about some problems from the theory of holomorphic functions on Banach spaces which have attracted the attention of many researchers during the last thirty years.

This paper studies timelike minimal surfaces in the De Sitter space $$\mathbb S^3_1(1) \subset \mathbb R^4_1$$ via a complex variable. Using analysis and stereographic projection of lightlike vectors C \cup \{\infty \}$$ , we obtain representation formula, together with some results about existence convenient isotropic coordinates. allows us to construct S^3_1(1)$$ local solutions certain PDE v...

defines a holomorphic function of z on the complement of the support of μ. For simplicity, let us restrict our attention to measures with compact support in C, although one can also make sense of Cauchy integrals of measures with noncompact support and infinite mass under suitable conditions. In the classical situation where μ is supported on a nice curve, the Cauchy integral of μ has a jump di...