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We study two Bregman projection methods for solving variational inequality problems in real reflexive Banach spaces. Our methods have simple and elegant structures, and they require only one Bregman projection onto the feasible set and one evaluation of the cost operator at each iteration. We prove that these methods converge weakly when the cost operator is pseudomonotone on the entire space and that they converge strongly when the cost operator is strongly pseudomonotone only on the feasible set. Extensions of our proposed methods to mixed variational inequality problems are also given. Finally, we consider some examples regarding the implementation of our methods in comparisons with known methods in the literature. [ABSTRACT FROM AUTHOR]

We consider a Dirichlet elliptic equation driven by the (p , q) -Laplacian and a reaction which includes a singular term, a parametric convection and a Carathéodory perturbation. Under minimal conditions on the perturbation, using the theory of nonlinear operators of pseudomonotone type, we show that for all small values of the parameter, the problem has a positive solution and determines the properties of the solution set. [ABSTRACT FROM AUTHOR]

In this paper, we study some operator theoretical properties of pseudo-differential operators with operator-valued symbols on the Heisenberg motion group. Specifically, we investigate L 2 – L p boundedness of pseudo-differential operators on the Heisenberg motion group for the range 2 ≤ p ≤ ∞. We also provide a necessary and sufficient condition on the operator-valued symbols in terms of λ-Weyl transforms such that the corresponding pseudo-differential operators on the Heisenberg motion group are in the class of Hilbert–Schmidt operators. As a consequence, we obtain a characterization of the trace class pseudo-differential operators on the Heisenberg motion group and provide a trace formula for these trace class operators. [ABSTRACT FROM AUTHOR]

We study properties of pseudodifferential operators which arise in their use in boundary value problems. Smooth domains as well as intersections of smooth domains are considered. [ABSTRACT FROM AUTHOR]

In this paper, we study a class of pseudodifferential operators known as time-frequency localization operators, which depend on a symbol ς and two windows functions g 1 and g 2 . We first present some basic properties of the windowed Opdam–Cherednik transform. Then, we use modulation spaces associated with the Opdam–Cherednik transform as appropriate classes for symbols and windows and study the boundedness and compactness of the localization operators associated with the windowed Opdam–Cherednik transform on modulation spaces. Finally, we show that these operators are in the Schatten–von Neumann class. [ABSTRACT FROM AUTHOR]

The main objective of this paper is to enrich the theoretical system of the linear canonical Fourier transform (LCFT) by introducing the canonical potential J m , A and corresponding L p -Sobolev space. Moreover, the Schwartz-type space S A is introduced. Further, pseudo-differential operator (PDO) is defined and obtained its another integral representation. The L p -boundedness result for the pseudo-differential operator associated with the LCFT is discussed. Some applications of Sobolev-type spaces H A m , p and H A m , p are given. [ABSTRACT FROM AUTHOR]

In this paper, we are interested in operators arising from the product of a weighted composition operator and a maximal differential operator on the Fock space. Let T max and C u , φ denote a maximal differential operator and a weighted composition operator, respectively. We characterize some C -selfadjoint operators C u , φ T max with respect to special conjugations C . Moreover, we obtain a partial characterization of hermitian operator C φ T max . [ABSTRACT FROM AUTHOR]

In this paper, we study the time optimal control of a class of partial stochastic impulsive functional differential systems with pseudo almost periodic coefficients in the a-norm functional spaces. Firstly, the existence of p-mean piecewise pseudo almost periodic mild solutions for the impulsive stochastic control systems is investigated by utilising stochastic analysis, analytic semigroup, the fixed-point techniques with fractional power arguments. Secondly, the existence of time optimal pairs of a system governed by partial stochastic impulsive functional differential equations is also obtained. Finally, two examples are provided to illustrate the time optimal control problems of parabolic control system with pseudo almost periodic coefficients and impulses. [ABSTRACT FROM AUTHOR]

Let G be a compact Hausdorff group and H be a closed subgroup of G. In this paper, we show that every bounded linear operator T on L p (G / H) is a pseudo-differential operator with the symbol σ for 1 ≤ p < ∞. We present necessary and sufficient conditions on symbols to ensure that a bounded pseudo-differential operator on L 2 (G / H) is self-adjoint, normal and present explicit formula for their symbols. A necessary and sufficient condition is also given such that the bounded linear operators on L p (G / H) posses eigenvalues and eigenfunctions. [ABSTRACT FROM AUTHOR]

In this work, the quadratic-phase Fourier transform (QPFT) on Schwartz space is defined and its necessary results are derived, including adjoint formula, Parseval identity, and continuity property. Furthermore, the continuity property on tempered distribution space is discussed, and also an example of the QPFT is provided. The present analysis is applied to develop a new class of pseudo-differential operators and prove an important theorem on Schwartz space. The boundary value problems of generalized partial differential equations (i.e. generalized telegraph, wave, and heat equations) are discussed using QPFT, and graphical plots are provided. [ABSTRACT FROM AUTHOR]

In this paper, some elementary and useful terminologies associated to Lebedev–Skalskaya transform (LS-transform) are notified and then estimates for R κ 1 2 + i τ (x) , F κ 1 2 + i τ (x) , translation and convolution operators associated to LS-transform are obtained. The continuity of LS-transforms, translation and convolution operators on functions spaces S α , k , H α , k and G α , k are discussed. The continuity of pseudo-differential operators in terms of LS-transforms is discussed on functions spaces S α , k , H α , k , G α , k and Lebesgue space. At the end, an application of LS-transform is shown by solving a differential equation of convolution type. [ABSTRACT FROM AUTHOR]

Lutsky in 2008 and 2009, where they investigated the invertibility of parabolic pseudo-differential operators with rapidly growing symbols and obtained estimates of exponential behaviour of solutions of pseudo-differential operators with growing and discontinuous symbols. During several years which followed the defense of the PhD thesis there appeared Vladimir's publications presenting interesting results for quasi-elliptic pseudodifferential operators and on solvability of Cauchy and Goursat problems for parabolic pseudodifferential equations (1971-1979 and later on), on solvability difference-differential equations (1978-1985 and later on), on Fredholmness of elliptic pseudodifferential operators and associated boundary value problems on noncompact manifolds (papers of 1971-1979). In 1993 he defended his doctoral thesis "The method of limit operators in solvability of pseudo-differential equations and convolution equations". [Extracted from the article]

In this paper, we discuss a class of stochastic nonlinear partial differential equation of Burgers type driven by pseudo differential operator (Δ + Δ α) for α ∈ (0 , 2) , and fractional Brownian sheet. The existence and uniqueness of an Lp-valued (local) solution is established for the initial valued problem to the equation. [ABSTRACT FROM AUTHOR]