Abstract. Let dμ be a probability measure on the unit circle and dν be the measure formed by adding a pure point to dμ. We give a simple formula for the Verblunsky coefficients of dν based on a result of Simon. Then we consider dμ0, a probability measure on the unit circle with l Verblunsky coefficients (αn(dμ0)) ∞ n=0 of bounded variation. We insert m pure points to dμ, rescale, and form the p...

Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 6 January 2020Accepted: 07 December 2020Published online: 22 February 2021Keywordsmetric entropy, doubling dimension, total generalized variationAMS Subject Headings41A30, 35L02, 35L65Publication DataISSN (print): 0036-1410ISSN (online): 1095-7154Publisher: Society for In...

the idea of difference sequences of real (or complex) numbers was introducedby ki zmaz cite{kizmaz}. in this paper, using the difference operator and alacunary sequence, we introduce and examine the class of sequence $bv_{theta}left(  delta,mathcal{f}right)  .$ we study some of its properties likesolidity, symmetricity, etc.

We present a descriptive definition of a multidimensional generalized Riemann integral based on a concept of generalized absolute continuity for additive functions of sets of bounded variation.