On fractional uncertainty: a dyadic approach

ABSTRACT

The use of Haar wavelet analysis, instead of classical trigonometric analysis, provides inequalities which can be regarded as Heisenberg-type inequalities associated to fractional order quantum mechanics. The aim of this paper is to introduce and prove some of these lower order uncertainty estimates.

COMMUNICATED BY:

• Alexander Pankov

Keywords:

• The uncertainty principle
• Heisenberg's inequalities
• Haar system
• dyadic analysis

2010 Mathematics Subject Classifications:

• 26D15
• 42C40

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The work was supported by grant 3631-2015 of Agencia Nacional de Promoción Científica y Tecnológica and IMAL, CONICET, Universidad Nacional del Litoral.