Convolution Integral Operators in Variable Bounded Variation Spaces
Laura Angelonı, Nelson Merentes, Maira Valera-López
Abstract
Abstract Working in the frame of variable bounded variation spaces in the sense of Wiener, introduced by Castillo, Merentes, and Rafeiro, we prove convergence in variable variation by means of the classical convolution integral operators. In the proposed approach, a crucial step is the convergence of the variable modulus of smoothness for absolutely continuous functions. Several preliminary properties of the variable $$p(\cdot )$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>p</mml:mi><mml:mo>(</mml:mo><mml:mo>·</mml:mo><mml:mo>)</mml:mo></mml:mrow></mml:math> -variation are also presented.
Topics & Concepts
MathematicsBounded variationSmoothnessVariable (mathematics)Convergence (economics)Bounded functionVariation (astronomy)Convolution (computer science)Boundary (topology)Mathematical analysisAlgorithmComputer scienceArtificial intelligencePhysicsEconomic growthEconomicsAstrophysicsArtificial neural networkAdvanced Harmonic Analysis ResearchApproximation Theory and Sequence SpacesAdvanced Banach Space Theory