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Abstract: In this paper we provide an alternative method to construct the Fueter primitive of an axial monogenic function of degree k, which is complementary to the one used in [4]. As a byproduct, we obtain an explicit description of the kernel of the Fueter mapping. We also apply our method to obtain the Fueter primitives of the Cauchy kernels with singularities on the unit sphere. [Copyright &y& Elsevier]

Abstract: In this paper we prove the Poincaré Lemma for circulant matrices with entries and the Mittag–Leffler theorem for Hermitian monogenic matrix functions. We then prove algebraic and topological duality theorems for Hermitian monogenic matrix functions. Finally, we use one of these duality theorems to characterize the -module , where denotes the sheaf of Hermitian monogenic functions. These results extend and clarify those obtained in R. Abreu-Blaya et al. (2012) . [Copyright &y& Elsevier]

Abstract: The new notion of slice monogenic functions introduced in the paper [F. Colombo, I. Sabadini, D.C. Struppa, Slice monogenic functions, Israel J. Math. 171 (2009) 385–403] led us to define a new functional calculus for an n-tuple of not necessarily commuting operators, see [F. Colombo, I. Sabadini, D.C. Struppa, A new functional calculus for noncommuting operators, J. Funct. Anal. 254 (2008) 2255–2274]. In this paper we prove a Cauchy formula with slice monogenic kernel for the slice monogenic functions. This new Cauchy formula is the fundamental tool to prove that our functional calculus apply to a more general setting. Moreover, we deduce some fundamental properties of the functional calculus, for example: some algebraic properties, the Spectral Mapping Theorem and the Spectral Radius Theorem. [ABSTRACT FROM AUTHOR]

Abstract: We consider a quasilinear integrodifferential system in non-normal form. Such a system is a generalization of a phase-field model with memory and includes, as a particular case, the system describing the combustion of a material with memory. In this paper, we study both the direct and the inverse problems. Our fundamental tools are: the theory of analytic semigroups, optimal regularity results and fixed point arguments. [Copyright &y& Elsevier]

We first review realizations of Herglotz functions in the unit ball of C N and provide new insights. Then, we define the corresponding class and prove the extend the results in the case of several quaternionic variables. [ABSTRACT FROM AUTHOR]

We define and study the counterparts of Gleason's problem, of the Drury–Arveson's space and of Schur multipliers when the unit ball of C N is replaced by the unit ball of H N , where H denotes the algebra of real quaternions. Schur multipliers are characterized in terms of coisometric operator matrices in quaternionic spaces. Finally, we define the counterpart of Blaschke factors in this setting and study a one point interpolation problem. [ABSTRACT FROM AUTHOR]