@article{GK_NK_2020, title={ANECESSARY AND REQUIRED CONDITION OF HAMBURGER MOMENT PROBLEM}, volume={8}, url={https://innovareacademics.in/journals/index.php/ijs/article/view/38523}, abstractNote={<p><strong>Objective: </strong>This present paper deals with necessary condition of Hamburger moment problem and polynomial which is not identically and non-negative sequence and semi-definite nature of a moment sequence.</p> <p><strong>Materials and Methods: </strong>If we suppose that (sn)n>=0 is a sequence of real numbers, the moment problem on I consists of solving the following three problems:</p> <p> There exists a positive measure on I with moment(sn)n>=0.</p> <p> This positive measure uniquely determined by the moments(sn)n>=0.</p> <p> The moment problem on [0,1) is referred to as Hausdroff moment problem and the moment problem on R is called Hamburger moment problem and the [0, ∞) is called Stieltjes moment problem.</p> <p> </p> <p><strong>Results: </strong>For n be an arbitrary non-negative integer, and sub-interval tn in every sub-interval is not greater than such that . The function V(t) in terms of operator M is ifα(t) had infinitely many points of non-decrease, then for every positive polynomial P(t) not identically zero, 21 TT n n μ t d t 2 t d t t t t 1p 0 i TT n i 1 i n 1 i 21 </p> <p>. . 2 μ μ μ t V M m 20 n n0 k k k 0t d t P μ t P M</p> <p><strong>Conclusion</strong>: For increasing function α(t) has a finite number of points of non-increase. Every non-negative sequence is either definite or semi-definite.</p>}, number={7}, journal={Innovare Journal of Sciences}, author={GK, SANAP and NK, RAUT}, year={2020}, month={May}, pages={32-36} }