Potential theory is important in the theory of subharmonic and $\delta$-subharmonic functions. In the article we sharpen Azarin's variant on the convergence of the sequence of canonical potentials in the space $L_{1,loc}(\mathbb{C})$.
Keywords: canonical potential; Radon measure; widely convergence.
2010 Mathematics Subject Classification: 31A05, 31B05. [ Full-text available (PDF) ] Top of the page.
A new multiplicative decomposition of the resolvent matrix of the truncated Hausdorff matrix moment (THMM) problem in the case of an odd and even number of moments via new Dyukarev-Stieltjes matrix (DSM) parameters is attained. Additionally, we derive Blaschke-Potapov factors of auxiliary resolvent matrices; each factor is decomposed with the help of the DSM parameters.
Keywords: Orthogonal matrix polynomial; Dyukarev-Stieltjes parameter; Resolvent matrix; Continued fractions.
2010 Mathematics Subject Classification: 30E05, 42C05, 47A56, 30B70. [ Full-text available (PDF) ] Top of the page.
We found quivers classes with ordinary weight functions and quivers for which there are not ordinary weight functions.
Keywords: exponent matrix; weight function of admissible quiver; rigid quiver.
2010 Mathematics Subject Classification: 16G20, 16G30. [ Full-text available (PDF) ] Top of the page.
In this article are obtained conditions when the derivative of a continuous almost automorphic (an asymptotically almost automorphic, an almost periodic, an asymptotically almost periodic) function remains a continuous almost automorphic (an asymptotically almost automorphic, an almost periodic, an asymptotically almost periodic) function, respectively.
Keywords: derivative; an almost automorphic; an asymptotically almost automorphic function.
2010 Mathematics Subject Classification: 43A60. [ Full-text available (PDF) ] Top of the page.
Constructive conditions for solvability are obtained, as well as an iterative scheme for finding solutions of the nonlinear equation that generalize the well-known Newton-Kantorovich theorem. The case of a nonlinear equation whose dimension does not coincide with the dimension of the unknown has been researched.
Keywords: Newton-Kantorovich method; iterative scheme; nonlinear equation; pseudoinverse matrices.
2010 Mathematics Subject Classification: 15A24; 34A15; 34C25. [ Full-text available (PDF) ] Top of the page.