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Register a new userOn neighborhood and partial sums problem for generalized Sakaguchi type functions
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In the present investigation, we introduce a new class k-US_{s}^{{eta}}({lambda},{mu},{gamma},t) of analytic functions in the open unit disc U with negative coefficients. The object of the present paper is to determine coefficient estimates, neighborhoods and partial sums for functions f(z) belonging to this class.
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V. Nestoridis conjectured that if $Omega$ is a simply connected subset of $mathbb{C}$ that does not contain $0$ and $S(Omega)$ is the set of all functions $fin mathcal{H}(Omega)$ with the property that the set $left{T_N(f)(z)coloneqqsum_{n=0}^Ndfrac{f^{(n)}(z)}{n!} (-z)^n : N = 0,1,2,dots right}$ is dense in $mathcal{H}(Omega)$, then $S(Omega)$ is a dense $G_delta$ set in $mathcal{H}(Omega)$. We answer the conjecture in the affirmative in the special case where $Omega$ is an open disc $D(z_0,r)$ that does not contain $0$.
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P.G. Grinevich L.D. Landau Institute forn Theoretical Physics
, Lomonosov Moscow State University
2015
We continue the studies of Moutard-type transform for generalized analytic functions started in our previous paper: arXiv:1510.08764. In particular, we suggest an interpretation of generalized analytic functions as spinor fields and show that in the framework of this approach Moutard-type transforms for the aforementioned functions commute with holomorphic changes of variables.
In the present investigation our main aim is to give lower bounds for the ratio of some normalized $q$-Bessel functions and their sequences of partial sums. Especially, we consider Jacksons second and third $q$-Bessel functions and we apply one normalization for each of them.
We study Sobolev estimates for solutions of the inhomogenous Cauchy-Riemann equations on annuli in $cx^n$, by constructing exact sequences relating the Dolbeault cohomology of the annulus with respect to Sobolev spaces of forms with those of the envelope and the hole. We also obtain solutions with prescibed support and estimates in Sobolev spaces using our method.
A smooth, strongly $mathbb{C}$-convex, real hypersurface $S$ in $mathbb{CP}^n$ admits a projective dual CR structure in addition to the standard CR structure. Given a smooth function $u$ on $S$, we provide characterizations for when $u$ can be decomposed as a sum of a CR function and a dual CR function. Following work of Lee on pluriharmonic boundary values, we provide a characterization using differential forms. We further provide a characterization using tangential vector fields in the style of Audibert and Bedford.
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