Examining commonly used equations for estimating the glomerular filtration rate (GFR) in a healthy cohort of children and adolescents [PDF]
BMC NephrologyBackground In this study, we compared established equations for estimating the glomerular filtration rate (GFR) in a cohort of apparently healthy children and adolescents and aimed to evaluate the equations’ validity.
Luise Trenkmann +5 more
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An embedding of Schwartz distributions in the algebra of asymptotic functions
International Journal of Mathematics and Mathematical Sciences, 1998 We present a solution of the problem of multiplication of Schwartz distributions by embedding the space of distributions into a differential algebra of generalized functions, called in the paper asymptotic function, similar to but different from J.
Michael Oberguggenberger +1 more
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On the Schwartz Distribution Approach to Local Volatility for European Option in a Generalised Jump Model with Stochastic Interest Rate [PDF]
EntropyThe Dupire formula is commonly regarded as a convenient analytical tool for the valuation of financial derivatives. In this paper, we continue the analytical treatment developed in our previous papers, deriving the aforementioned formula for the European
Piotr Nowak, Dariusz Gatarek
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The Distributional Stress–Energy Quadrupole and Gravitational Waves
Universe, 2023 In this overview, we discuss the (Schwartz) distributional stress–energy quadrupole and show it is a source of gravitational waves. We provide an explicit formula for the metric of linearised gravity in the case of a background Minkowski spacetime.
Jonathan Gratus, Spyridon Talaganis
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Stability of Trigonometric Functional Equations in Generalized Functions
Journal of Inequalities and Applications, 2010 We consider the Hyers-Ulam stability of a class of trigonometric functional equations in the spaces of generalized functions such as Schwartz distributions, Fourier hyperfunctions, and Gelfand generalized functions.
Jeongwook Chang, Jaeyoung Chung
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Regularity of nonlinear generalized functions: A counterexample in the nonstandard setting
Examples and Counterexamples, 2021 Regularity theory in generalized function algebras of Colombeau type is largely based on the notion of G∞-regularity, which reduces to C∞-regularity when restricted to Schwartz distributions.
H. Vernaeve
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Polynomial tempered distributions
Karpatsʹkì Matematičnì Publìkacìï, 2013 In the article polynomial (nonlinear) analogue of tempered Schwartz distributions is constructed. Generalized operation of differentiation in the space of polynomial generalized functions as well as Fourier-Laplace transformation of such distributions ...
S. V. Sharyn
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ASYMPTOTIC ALMOST AUTOMORPHY OF FUNCTIONS AND DISTRIBUTIONS
Ural Mathematical Journal, 2020 This work aims to introduce and to study asymptotic almost automorphy in the context of Sobolev–Schwartz distributions. Applications to linear ordinary differential equation and neutral difference differential equations are also given.
Chikh Bouzar, Fatima Zahra Tchouar
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Ulam Problem for the Cosine Addition Formula in Sato Hyperfunctions
Journal of Function Spaces, 2015 We prove the Ulam problem for the cosine addition formula in the spaces of Schwartz distributions and Sato hyperfunctions with respect to bounded distributions and bounded hyperfunctions.
Jaeyoung Chung, Soon-Yeong Chung
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Further Results on Colombeau Product of Distributions
International Journal of Mathematics and Mathematical Sciences, 2013 Results on Colombeau product of distributions and are derived. They are obtained in Colombeau differential algebra of generalized functions that contains the space of Schwartz distributions as a subspace and has a notion of “association” that is a ...
Biljana Jolevska-Tuneska +1 more
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