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Matrix Weighted Kolmogorov–Riesz’s Compactness Theorem
In this paper, several versions of the Kolmogorov–Riesz compactness theorem in weighted Lebesgue spaces with matrix weights are obtained. In...
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On the Solution to the Kolmogorov-Feller Equation Arising in a Biological Evolution Model
AbstractThe paper considers Kolmogorov–Feller equation for the probability density of a Markov process on a half-axis, which arises in important...
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Quasi-Invariance for Infinite-Dimensional Kolmogorov Diffusions
We prove Cameron-Martin type quasi-invariance for the heat kernel measure of infinite-dimensional Kolmogorov and similar degenerate diffusions. We...
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Pointwise and weighted Hessian estimates for Kolmogorov–Fokker–Planck-type operators
In this article, we obtain Hessian estimates for Kolmogorov–Fokker–Planck operators in non-divergence form in several Banach function spaces. Our...
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Translation beyond Delsarte
We introduce general translations as solutions to Cauchy or Dirichlet problems. This point of view allows us to handle for instance the...
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Andrei Kolmogorov and Leonid Levin on Randomness
This chapter provides a translation of a letter written in 1939, in which Andrei Kolmogorov’s explains his views on the connection between...
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On the Relationship between Sharp Kolmogorov-Type Inequalities and Sharp Kolmogorov–Remez-Type Inequalities
We establish a new theorem on the relationship between sharp constants in Kolmogorov-type inequalities and sharp constants in Kolmogorov–Remez-type...
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New Perspectives on Recent Trends for Kolmogorov Operators
After carrying out an overview on the non Euclidean geometrical setting suitable for the study of Kolmogorov operators with rough coefficients, we...
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Approximate Analytical Solution of the Generalized Kolmogorov-Petrovsky-Piskunov Equation with Cubic Nonlinearity
In this paper, the approximate analytical oscillatory solutions to the generalized Kolmogorov-Petrovsky-Piskunov equation (gKPPE for short) are...
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Kolmogorov Widths of the Nikol’skii–Besov Classes of Periodic Functions of Many Variables in the Space of Quasicontinuous Functions
We obtain order estimates for the M -dimensional Kolmogorov widths of the Nikol’skii–Besov classes of periodic functions of many variables with...
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Riesz–Kolmogorov Type Compactness Criteria in Function Spaces with Applications
We present forms of the classical Riesz–Kolmogorov theorem for compactness that are applicable in a wide variety of settings. In particular, our...
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Correct Solvability of the Cauchy Problem and Integral Representations of the Solutions for Ultraparabolic Kolmogorov-Type Equations with Two Groups of Spatial Variables of Degeneration
We establish some properties of the classical fundamental solution of the Cauchy problem for an inhomogeneous ultraparabolic Kolmogorov-type equation...
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Solving Non-linear Kolmogorov Equations in Large Dimensions by Using Deep Learning: A Numerical Comparison of Discretization Schemes
Non-linear partial differential Kolmogorov equations are successfully used to describe a wide range of time dependent phenomena, in natural sciences,...
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Fundamental Solution of the Cauchy Problem for Degenerate Parabolic Kolmogorov-Type Equations of Any Order
We consider degenerate parabolic Kolmogorov-type equations of any order with two groups of spatial variables of degeneration and coefficients...
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Fréchet-Kolmogorov compactness of Prabhakar integral operator
In many cases, the differential equations are converted into an equivalent functional equations involving integral operators generated by different...
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Chebyshev Wavelets Collocation Method for Extended Fisher Kolmogorov Equations One and Two Space Dimension
In this study, Chebyshev wavelet collocation method has been applied to obtain approximate solution of nonlinear partial differential equations....
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Well-Posedness and Singularity Formation for the Kolmogorov Two-Equation Model of Turbulence in 1-D
We study the Kolomogorov two-equation model of turbulence in one space dimension. Two are the main results of the paper. First of all, we establish a...
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Schauder Estimates for Kolmogorov-Fokker-Planck Operators with Coefficients Measurable in Time and Hölder Continuous in Space
We consider degenerate Kolmogorov-Fokker-Planck operators $$\mathcal...