# Nonharmonic analysis of boundary value problems without WZ condition

@article{Ruzhansky2016NonharmonicAO,
title={Nonharmonic analysis of boundary value problems without WZ condition},
author={Michael Ruzhansky and Niyaz Tokmagambetov},
journal={Mathematical Modelling of Natural Phenomena},
year={2016},
volume={12},
pages={115-140}
}
• Published 2016
• Mathematics
• Mathematical Modelling of Natural Phenomena
In this work we continue our research on nonharmonic analysis of boundary value problems as initiated in [8]. There, we assumed that the eigenfunctions of the model operator on which the construction is based do not have zeros. In this paper we have weakened this condition extending the applicability of the developed pseudo-differential analysis. Also, we do not assume that the underlying set Omega is bounded.
36 Citations
Global Functional calculus, lower/upper bounds and evolution equations on manifolds with boundary
• Mathematics
• 2021
Given a smooth manifold M (with or without boundary), in this paper we establish a global functional calculus (without the standard assumption that the operators are classical pseudo-differentialExpand
Spectral properties of the iterated Laplacian with a potential in a punctured domain
In the work we derive regularized trace formulas which were established in papers of Kanguzhin and Tokmagambetov for the Laplace and m-Laplace operators in a punctured domain with the fixed iteratingExpand
Green's formula for integro-differential operators
• Mathematics
• 2018
Abstract In this report we establish Green's formula for an integro-differential operator, and apply it to describe a class of self-adjoint fractional order differential operators. A found symmetricExpand
On a non–local problem for a multi–term fractional diffusion-wave equation
• Mathematics
• 2018
Abstract This paper deals with the multi-term generalisation of the time-fractional diffusion-wave equation for general operators with discrete spectrum, as well as for positive hypoellipticExpand
L∞-BMO bounds for pseudo-multipliers associated with the harmonic oscillator
• 2021
In this note we investigate some conditions of Hörmander-Mihlin type in order to assure the L∞-BMO boundedness for pseudo-multipliers of the harmonic oscillator. The H-L continuity for HermiteExpand
Formulas for the eigenvalues of the iterated Laplacian with singular potentials
In this work we give some identities for the eigenvalues of the iterated Laplacian with a potential in a punctured domain. Moreover, we discuss some techniques to study spectral properties of theseExpand
Remark on a Regularized Trace Formula for m -Laplacian in a Punctured Domain
• Mathematics
• 2017
In this paper we extend results on regularized trace formulae which were established in [9, 10] for the Laplace and m-Laplace operators in a punctured domain with the fixed iterating order $$m\inExpand On nonlinear damped wave equations for positive operators. I. Discrete spectrum • Mathematics • 2017 In this paper we study a Cauchy problem for the nonlinear damped wave equations for a general positive operator with discrete spectrum. We derive the exponential in time decay of solutions to theExpand Expansion of traces and Dixmier traceability for global pseudo-differential operators on manifolds with boundary • Mathematics • 2021 Given a smooth manifold M (with or without boundary), in this paper we study the regularisation of traces for the global pseudo-differential calculus in the context of non-harmonic analysis. Indeed,Expand Remark on the Eigenvalues of the m-Laplacian in a Punctured Domain In this paper, we prove some identities for the eigenvalues of the m-Laplacian in a punctured domain. Also, we discuss possible techniques to investigate spectral properties of the operators inExpand #### References SHOWING 1-10 OF 16 REFERENCES Nonharmonic Analysis of Boundary Value Problems • Mathematics • 2015 In this paper, we develop the global symbolic calculus of pseudo-differential operators generated by a boundary value problem for a given (not necessarily self-adjoint or elliptic) differentialExpand Pseudo-differential operators generated by a non-local boundary value problem • Mathematics • 2015 Pseudo-differential operators and -toroidal symbols generated by a non-local boundary value problem are investigated. A formula for compositions with pseudo-differential operators generated by aExpand Wave equation for sums of squares on compact Lie groups • Mathematics • 2015 In this paper we investigate the well-posedness of the Cauchy problem for the wave equation for sums of squares of vector fields on compact Lie groups. We obtain the loss of regularity for solutionsExpand Very weak solutions of wave equation for Landau Hamiltonian with irregular electromagnetic field • Physics, Mathematics • 2016 In this paper, we study the Cauchy problem for the Landau Hamiltonian wave equation, with time-dependent irregular (distributional) electromagnetic field and similarly irregular velocity. For suchExpand On the Fourier analysis of operators on the torus • Mathematics • 2006 Basic properties of Fourier integral operators on the torus \( \mathbb{T}^n = (\mathbb{R}/2\pi \mathbb{Z})^n$$ are studied by using the global representations by Fourier series instead of localExpand
Schatten classes, nuclearity and nonharmonic analysis on compact manifolds with boundary
• Mathematics
• 2015
Given a compact manifold $M$ with boundary $\partial M$, in this paper we introduce a global symbolic calculus of pseudo-differential operators associated to $(M,\partial M)$. The symbols ofExpand
Hörmander Class of Pseudo-Differential Operators on Compact Lie Groups and Global Hypoellipticity
• Mathematics
• 2014
In this paper we give several global characterisations of the Hörmander class $$\Psi ^m(G)$$Ψm(G) of pseudo-differential operators on compact Lie groups in terms of the representation theory of theExpand
On the Toroidal Quantization of Periodic Pseudo-Differential Operators
• Mathematics
• 2009
On the torus, pseudo-differential operators can be presented globally by Fourier series, without local coordinate charts. Periodization of partial differential equations leads to investigating theExpand
The Fourier transform and convolutions generated by a differential operator with boundary condition on a segment
• Mathematics
• 2014
We introduce the concepts of the Fourier transform and convolution generated by an arbitrary restriction of the differentiation operator in the space L 2(0, b). In contrast to the classicalExpand
Fourier multipliers, symbols, and nuclearity on compact manifolds
• Mathematics
• 2014
The notion of invariant operators, or Fourier multipliers, is discussed for densely defined operators on Hilbert spaces, with respect to a fixed partition of the space into a direct sum ofExpand