Results 41 to 50 of about 9,965 (190)
Mathematical Methods in the Applied Sciences, Volume 48, Issue 13, Page 12654-12674, September 2025.ABSTRACT We have studied possible applications of a particular pseudodifferential algebra in singular analysis for the construction of fundamental solutions and Green's functions of a certain class of elliptic partial differential operators. The pseudodifferential algebra considered in the present work, comprises degenerate partial differential ...
Heinz‐Jürgen Flad +1 more
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Kipriyanov-Katrakhov singular pseudodifferential operators
Современная математика: Фундаментальные направленияSingular pseudodifferential operators created on the base of the mixed Fourier–Bessel transform are usually called Kipriyanov singular pseudodifferential operators (SPDO). The paper provides an overview of three types of such operators.
L. N. Lyakhov +2 more
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Asymptotics for the Ostrovsky-Hunter Equation in the Critical Case
International Journal of Differential Equations, 2017 We consider the Cauchy problem for the Ostrovsky-Hunter equation ∂x∂tu-b/3∂x3u-∂xKu3=au, t,x∈R2, u0,x=u0x, x∈R, where ab>0. Define ξ0=27a/b1/4. Suppose that K is a pseudodifferential operator with a symbol K^ξ such that K^±ξ0=0, Im K^ξ=0, and K^ξ≤C. For
Fernando Bernal-Vílchis +2 more
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An exotic calculus of Berezin–Toeplitz operators
Mathematika, Volume 71, Issue 2, April 2025.Abstract We develop a calculus of Berezin–Toeplitz operators quantizing exotic classes of smooth functions on compact Kähler manifolds and acting on holomorphic sections of powers of positive line bundles. These functions (classical observables) are exotic in the sense that their derivatives are allowed to grow in ways controlled by local geometry and ...
Izak Oltman
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On some analytical index formulas related to operator-valued symbols
Electronic Journal of Differential Equations, 2002 For several classes of pseudodifferential operators with operator-valued symbol analytic index formulas are found. The common feature is that usual index formulas are not valid for these operators.
Grigori Rozenblum
doaj
The K-theory of bisingular pseudodifferential algebras
, 2015 In this paper we calculate the K-theory of $C^{\ast}$-algebras given by the norm-closures of spaces of bisingular pseudodifferential operators.
Bohlen, Karsten
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Decoupling for Schatten class operators in the setting of quantum harmonic analysis
Bulletin of the London Mathematical Society, Volume 57, Issue 1, Page 23-37, January 2025.Abstract We introduce the notion of decoupling for operators, and prove an equivalence between classical ℓqLp$\ell ^qL^p$ decoupling for functions and ℓqSp$\ell ^q{\mathcal {S}}^p$ decoupling for operators on bounded sets in R2d${\mathbb {R}}^{2d}$. We also show that the equivalence depends only on the bounded set Ω$\Omega$ and not on the values of p,q$
Helge J. Samuelsen
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Elliptic operators on refined Sobolev scales on vector bundles
Open Mathematics, 2017 We introduce a refined Sobolev scale on a vector bundle over a closed infinitely smooth manifold. This scale consists of inner product Hörmander spaces parametrized with a real number and a function varying slowly at infinity in the sense of Karamata. We
Zinchenko Tetiana
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TASK Quarterly, 2017 We consider a generalization of the projection operator method for the case of the Cauchy problem in 1D space for systems of evolution differential equations of first order with variable coefficients.
SERGEY LEBLE, IRINA VERESHCHAGINA
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Journal of Mathematics, Volume 2025, Issue 1, 2025.Recent research has introduced piecewise fractional differential equations—particularly within deterministic‐stochastic frameworks—to better model complex and real‐world phenomena. However, their application to modeling the progression and treatment of diabetes remains limited.
Muner M. Abou Hasan +5 more
wiley +1 more source