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Quasiconformal deformation of the chordal Loewner driving function and first variation of the Loewner energy. [PDF]
Math AnnSung J, Wang Y.
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Regularization by Noise of an Averaged Version of the Navier-Stokes Equations. [PDF]
J Dyn Differ EquLange T.
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On the existence of ψ-integrals
Rendiconti del Circolo Matematico di Palermo, 1972The approximating sums for the Riemann-Stieltjes integral are formed with the integrand function evaluated at an arbitrary point in each subdivision interval. The ψ-integral uses the idea of achoice function to select a particular point in each of these intervals.
Baker, James D., Shive, Robert A. jun.
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Ukrainian Mathematical Journal, 2004
Summary: We find asymptotic formulas for the least upper bounds of the deviations of Fourier operators on classes of functions locally summable on the entire real axis and defined by \(\overline{\Psi}\)-integrals. On these classes, we also obtain asymptotic equalities for the upper bounds of functionals that characterize the simultaneous approximation ...
Stepanets', O. I., Sokolenko, I. V.
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Summary: We find asymptotic formulas for the least upper bounds of the deviations of Fourier operators on classes of functions locally summable on the entire real axis and defined by \(\overline{\Psi}\)-integrals. On these classes, we also obtain asymptotic equalities for the upper bounds of functionals that characterize the simultaneous approximation ...
Stepanets', O. I., Sokolenko, I. V.
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Ukrainian Mathematical Journal, 2001
Under certain conditions on the sequences \(\overline{\psi}=(\{\psi_1(k)\}, \{\psi_2(k)\}),\) \(\Lambda=\{\lambda_k^{(n)}\}\), \(k,n=0,1,2,...\), the asymptotic formulas for the quantities \[ {\mathcal E}(C_\infty^{\overline{\psi}};U_n)= \sup_{f\in C_\infty^{\overline{\psi}}} \|f(x)-U_n(f,x,\Lambda)\|_{C} \] are obtained as \(n\to\infty\).
Rukasov, V. I., Chajchenko, S. O.
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Under certain conditions on the sequences \(\overline{\psi}=(\{\psi_1(k)\}, \{\psi_2(k)\}),\) \(\Lambda=\{\lambda_k^{(n)}\}\), \(k,n=0,1,2,...\), the asymptotic formulas for the quantities \[ {\mathcal E}(C_\infty^{\overline{\psi}};U_n)= \sup_{f\in C_\infty^{\overline{\psi}}} \|f(x)-U_n(f,x,\Lambda)\|_{C} \] are obtained as \(n\to\infty\).
Rukasov, V. I., Chajchenko, S. O.
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Ukrainian Mathematical Journal, 2005
Summary: We obtain asymptotic equalities for deviations of rectangular linear means of Fourier series on classes of \(\overline{\psi}\)-integrals of functions of many variables.
Rukasov, V. I. +2 more
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Summary: We obtain asymptotic equalities for deviations of rectangular linear means of Fourier series on classes of \(\overline{\psi}\)-integrals of functions of many variables.
Rukasov, V. I. +2 more
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Ukrainian Mathematical Journal, 1998
Let \(L\) be the space of \(2\pi\)-periodic integrable functions. Let \(S[f]= {a_{0}/2}+\sum\limits_{k=1}^{\infty} (a_{k}\cos kx+b_{k}\sin kx)\equiv\sum\limits_{k=1}^{\infty}A_{k}(f;x)\) be the Fourier series of the function \(f\in L\), \(S_{n}(f;x)=\sum\limits_{k=1}^{n} A_{k}(f;x)\), and let \(\rho_{n}(f;x)=f(x)-S_{n-1}(f;x)\). Let \(\bar\psi=(\psi_{1}
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Let \(L\) be the space of \(2\pi\)-periodic integrable functions. Let \(S[f]= {a_{0}/2}+\sum\limits_{k=1}^{\infty} (a_{k}\cos kx+b_{k}\sin kx)\equiv\sum\limits_{k=1}^{\infty}A_{k}(f;x)\) be the Fourier series of the function \(f\in L\), \(S_{n}(f;x)=\sum\limits_{k=1}^{n} A_{k}(f;x)\), and let \(\rho_{n}(f;x)=f(x)-S_{n-1}(f;x)\). Let \(\bar\psi=(\psi_{1}
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Rate of convergence of Fourier series on the classes of $$\bar \Psi $$ -integrals-integrals
Ukrainian Mathematical Journal, 1997We introduce the notion of $$\bar \Psi $$ -integrals of 2π-periodic summable functions f, f e L, on the basis of which the space L is decomposed into subsets (classes) $$L^{\bar \Psi } $$
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Ukrainian Mathematical Journal, 1998
We investigate the rate of convergence of Fourier series on the classes \(L^{\bar \psi } \)N in the uniform and integral metrics. The results obtained are extended to the case where the classes \(L^{\bar \psi } \)N are the classes of convolutions of functions from N with kernels with slowly decreasing coefficients.
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We investigate the rate of convergence of Fourier series on the classes \(L^{\bar \psi } \)N in the uniform and integral metrics. The results obtained are extended to the case where the classes \(L^{\bar \psi } \)N are the classes of convolutions of functions from N with kernels with slowly decreasing coefficients.
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Constructing Integrable Lindblad Superoperators
Physical Review Letters, 2021Balázs Pozsgay +2 more
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