On the convergence properties of basic series representing Clifford valued functions.
On the growth of the resolvent operators for power bounded operators
Outline. In this paper I discuss some quantitative aspects related to power bounded operators T and to the decay of . For background I refer to two recent surveys J. Zemánek [1994], C. J. K. Batty [1994]. Here I try to complement these two surveys in two different directions. First, if the decay of is as fast as O(1/n) then quite strong conclusions can be made. The situation can be thought of as a discrete version of analytic semigroups; I try to motivate this in Section 1 by demonstrating the...
On the Multiplicity of an Analytic Operator-Valued Function.
On the periodicity of trigonometric functions generalized to quotient rings of R[x]
We apply a method of Euler to algebraic extensions of sets of numbers with compound additive inverse which can be seen as quotient rings of R[x]. This allows us to evaluate a generalization of Riemann’s zeta function in terms of the period of a function which generalizes the function sin z. It follows that the functions generalizing the trigonometric functions on these sets of numbers are not periodic.
On the possibility of extending a function from a part of a domain to a generalized analytic function on this domain.
On the sense preserving mappings in the Helm topology in the plane
∗Research supported by the grant No. GAUK 186/96 of Charles University.We introduce the helm topology in the plane. We show that (assuming the helm local injectivity and the Euclidean continuity) each mapping which is oriented at all points of a helm domain U is oriented at U.
On the Singularities of Functions with Values in a Clifford Algebra.
On the trajectories of a quadratic differential, I.
On the zeros of a quaternionic polynomial: An extension of the Eneström-Kakeya theorem
We present some results on the location of zeros of regular polynomials of a quaternionic variable. We derive new bounds of Eneström-Kakeya type for the zeros of these polynomials by virtue of a maximum modulus theorem and the structure of the zero sets of a regular product established in the newly developed theory of regular functions and polynomials of a quaternionic variable. Our results extend some classical results from complex to the quaternionic setting as well.
On vector-valued analytic functions with constant norm
Oscillatory properties of second order linear differential equations in the complex domain
-adic analysis and Bell numbers of two variables. (Analyse -adique et nombres de Bell à deux variables.)
-adic analytic interpolation
Pairs of Clifford algebras of the Hurwitz type
For a given Hurwitz pair the existence of a bilinear mapping (where and ) denote the Clifford algebras of the quadratic forms and , respectively) generated by the Hurwitz multiplication “o” is proved and the counterpart of the Hurwitz condition on the Clifford algebra level is found. Moreover, a necessary and sufficient condition for "⭑" to be generated by the Hurwitz multiplication is shown.
Plane elliptic systems and monogenic functions in symmetric domains
Plane wave decompositions of monogenic functions
Plane waves, biregular functions and hypercomplex Fourier analysis
Pluriregular, plurigeneralized regular equations in Clifford analysis.
Polygone de Newton et théorème de préparation
Prolongement analytique en analyse -adique