scholarly journals L P LOCAL UNCERTAINTY INEQUALITY FOR THE STURM-LIOUVILLE TRANSFORM

Cubo (Temuco) ◽  
2014 ◽  
Vol 16 (1) ◽  
pp. 95-104 ◽  
Author(s):  
Fethi Soltani
Keyword(s):  
Local Uncertainty ◽  
Sturm Liouville ◽  
Uncertainty Inequality

scholarly journals HEISENBERG–PAULI–WEYL UNCERTAINTY INEQUALITY FOR THE DUNKL TRANSFORM ON ℝd

2012 ◽  
Vol 87 (2) ◽  
pp. 316-325 ◽  
Author(s):  
FETHI SOLTANI
Keyword(s):  
Dunkl Transform ◽  
Local Uncertainty ◽  
Global Uncertainty ◽  
Uncertainty Inequality

AbstractIn this paper, we give analogues of the local uncertainty inequality for the Dunkl transform on ℝd, and indicate how the local uncertainty inequality implies a global uncertainty inequality.

A note on continuous fractional wavelet transform in ℝn

2021 ◽  
Author(s):  
Amit K. Verma ◽  
Bivek Gupta
Keyword(s):  
Wavelet Transform ◽  
Reproducing Kernel ◽  
Morrey Space ◽  
Inner Product ◽  
Dimensional Euclidean Space ◽  
Reconstruction Formula ◽  
Local Uncertainty ◽  
Fractional Wavelet Transform ◽  
Uncertainty Inequality ◽  
Product Relation

In this paper, we study the continuous fractional wavelet transform (CFrWT) in [Formula: see text]-dimensional Euclidean space [Formula: see text] with scaling parameter [Formula: see text] such that [Formula: see text]. We obtain inner product relation and reconstruction formula for the CFrWT depending on two wavelets along with the reproducing kernel function, involving two wavelets, for the image space of CFrWT. We obtain Heisenberg’s uncertainty inequality and Local uncertainty inequality for the CFrWT. Finally, we prove the boundedness of CFrWT on the Morrey space [Formula: see text] and estimate [Formula: see text]-distance of the CFrWT of two argument functions with respect to different wavelets.

Sturm-Liouville Problem for Stationary Differential Operator with Nonlocal Two-Point Boundary Conditions

2006 ◽  
Vol 11 (1) ◽  
pp. 47-78 ◽  
Author(s):  
S. Pečiulytė ◽  
A. Štikonas
Keyword(s):  
Boundary Condition ◽  
Differential Operator ◽  
Boundary Conditions ◽  
Nonlocal Boundary Condition ◽  
Nonlocal Boundary ◽  
Liouville Problem ◽  
Complex Case ◽  
Qualitative Behavior ◽  
Point Boundary ◽  
Sturm Liouville

The Sturm-Liouville problem with various types of two-point boundary conditions is considered in this paper. In the first part of the paper, we investigate the Sturm-Liouville problem in three cases of nonlocal two-point boundary conditions. We prove general properties of the eigenfunctions and eigenvalues for such a problem in the complex case. In the second part, we investigate the case of real eigenvalues. It is analyzed how the spectrum of these problems depends on the boundary condition parameters. Qualitative behavior of all eigenvalues subject to the nonlocal boundary condition parameters is described.

Sign in / Sign up

Export Citation Format

Share Document