An Note on Uncertainty Inequalities for Deformed Harmonic Oscillators

Saifallah Ghobber

doi:10.3390/sym11030335

An Note on Uncertainty Inequalities for Deformed Harmonic Oscillators

Symmetry ◽

10.3390/sym11030335 ◽

2019 ◽

Vol 11 (3) ◽

pp. 335 ◽

Cited By ~ 1

Author(s):

Saifallah Ghobber

Keyword(s):

Integral Operators ◽

Harmonic Oscillators ◽

Uncertainty Inequalities

The aim of this paper is to prove some uncertainty inequalities for a class of integral operators associated to deformed harmonic oscillators.

Download Full-text

Weighted estimates for a class of quasilinear integral operators

Sibirskii matematicheskii zhurnal ◽

10.33048/smzh.2019.60.209 ◽

2018 ◽

Vol 60 (2) ◽

pp. 376-390

Author(s):

A. A. Kalybay

Keyword(s):

Integral Operators ◽

Weighted Estimates

Download Full-text

Multianisotropic integral operators defined by regular equations

Sibirskii matematicheskii zhurnal ◽

10.33048/smzh.2019.60.310 ◽

2018 ◽

Vol 60 (3) ◽

pp. 610-629

Author(s):

G. A. Karapetyan ◽

H. A. Petrosyan

Keyword(s):

Integral Operators

Download Full-text

Pseudoinversion of Integral Operators in the Problems of Observation, Terminal Control, and Simulation of Dynamics of Distributed Parameter Systems

Journal of Automation and Information Sciences ◽

10.1615/jautomatinfscien.v31.i4-5.130 ◽

1999 ◽

Vol 31 (4-5) ◽

pp. 98-105

Author(s):

Vladimir Antonovich Stoyan

Keyword(s):

Integral Operators ◽

Distributed Parameter Systems ◽

Distributed Parameter ◽

Terminal Control

Download Full-text

Multi-parameter Singular Integrals II: General Theory

10.23943/princeton/9780691162515.003.0005 ◽

2017 ◽

Author(s):

Brian Street

Keyword(s):

General Theory ◽

Singular Integral ◽

Singular Integrals ◽

Integral Operators ◽

Singular Integral Operators ◽

Main Issue

This chapter turns to a general theory which generalizes and unifies all of the examples in the preceding chapters. A main issue is that the first definition from the trichotomy does not generalize to the multi-parameter situation. To deal with this, strengthened cancellation conditions are introduced. This is done in two different ways, resulting in four total definitions for singular integral operators (the first two use the strengthened cancellation conditions, while the later two are generalizations of the later two parts of the trichotomy). Thus, we obtain four classes of singular integral operators, denoted by A1, A2, A3, and A4. The main theorem of the chapter is A1 = A2 = A3 = A4; i.e., all four of these definitions are equivalent. This leads to many nice properties of these singular integral operators.

Download Full-text

The Calder´on-Zygmund Theory I: Ellipticity

10.23943/princeton/9780691162515.003.0001 ◽

2017 ◽

Author(s):

Brian Street

Keyword(s):

Classical Theory ◽

Singular Integral ◽

Singular Integrals ◽

Differential Operators ◽

Integral Operators ◽

Singular Integral Operators ◽

Single Parameter ◽

Partial Differential ◽

Translation Invariant ◽

Partial Differential Operators

This chapter discusses a case for single-parameter singular integral operators, where ρ‎ is the usual distance on ℝn. There, we obtain the most classical theory of singular integrals, which is useful for studying elliptic partial differential operators. The chapter defines singular integral operators in three equivalent ways. This trichotomy can be seen three times, in increasing generality: Theorems 1.1.23, 1.1.26, and 1.2.10. This trichotomy is developed even when the operators are not translation invariant (many authors discuss such ideas only for translation invariant, or nearly translation invariant operators). It also presents these ideas in a slightly different way than is usual, which helps to motivate later results and definitions.

Download Full-text