Results 41 to 50 of about 1,931 (172)

Fundamental Solutions and Green's Functions for Certain Elliptic Differential Operators From a Pseudodifferential Algebra

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, Gohar Flad‐Harutyunyan   +1 more
wiley   +1 more source

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
wiley   +1 more source

Microlocal properties of Shubin pseudodifferential and localization operators

, 2016
We investigate global microlocal properties of localization operators and Shubin pseudodifferential operators. The microlocal regularity is measured in terms of a scale of Shubin-type Sobolev spaces.
Wahlberg, Patrik, Schulz, René
core   +1 more source

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
wiley   +1 more source

Schrödinger operators with δ and δ′-potentials supported on hypersurfaces

, 2013
Self-adjoint Schrödinger operators with δ and δ′-potentials supported on a smooth compact hypersurface are defined explicitly via boundary conditions.
Lotoreichik, Vladimir, Behrndt, Jussi, Langer, Matthias   +2 more
core   +1 more source

Determinants of classical SG‐pseudodifferential operators [PDF]

Mathematische Nachrichten, 2013
We introduce a generalized trace functional TR in the spirit of Kontsevich and Vishik's canonical trace for classical SG‐pseudodifferential operators on and suitable manifolds, using a finite‐part integral regularization technique. This allows us to define a zeta‐regularized determinant for parameter‐elliptic operators , , . For , the asymptotics of
Maniccia, L., Schrohe, E., Seiler, J.
openaire   +2 more sources

A Novel Crossover Dynamics of Variable‐Order Fractal‐Fractional Stochastic Diabetes Model: Numerical Simulations

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, Ahlam M. Alghanmi, Seham M. AL-Mekhlafi, Hannah Al Ali, Zindoga Mukandavire, Rajashik Paul   +5 more
wiley   +1 more source

Conformally invariant random fields, Liouville quantum gravity measures, and random Paneitz operators on Riemannian manifolds of even dimension

Journal of the London Mathematical Society, Volume 110, Issue 5, November 2024.
Abstract For large classes of even‐dimensional Riemannian manifolds (M,g)$(M,g)$, we construct and analyze conformally invariant random fields. These centered Gaussian fields h=hg$h=h_g$, called co‐polyharmonic Gaussian fields, are characterized by their covariance kernels k which exhibit a precise logarithmic divergence: |k(x,y)−log1d(x,y)|≤C$\big ...
Lorenzo Dello Schiavo, Ronan Herry, Eva Kopfer, Karl‐Theodor Sturm   +3 more
wiley   +1 more source

The quantization of Maxwell theory in the Cauchy radiation gauge: Hodge decomposition and Hadamard states

Journal of the London Mathematical Society, Volume 110, Issue 5, November 2024.
Abstract The aim of this paper is to prove the existence of Hadamard states for the Maxwell equations on any globally hyperbolic spacetime. This will be achieved by introducing a new gauge fixing condition, the Cauchy radiation gauge, that will allow to suppress all the unphysical degrees of freedom. The key ingredient for achieving this gauge is a new
Simone Murro, Gabriel Schmid
wiley   +1 more source

The anisotropic Calderón problem at large fixed frequency on manifolds with invertible ray transform

Journal of the London Mathematical Society, Volume 110, Issue 4, October 2024.
Abstract We consider the inverse problem of recovering a potential from the Dirichlet to Neumann map at a large fixed frequency on certain Riemannian manifolds. We extend the earlier result of Uhlmann and Wang [arXiv:2104.03477] to the case of simple manifolds, and more generally to manifolds where the geodesic ray transform is stably invertible.
Shiqi Ma, Suman Kumar Sahoo, Mikko Salo
wiley   +1 more source