scholarly journals Orthonormal bases for anisotropic α-modulation spaces

2011 ◽  
Vol 63 (1) ◽  
pp. 109-121
Author(s):  
Kenneth N. Rasmussen
Keyword(s):  
Modulation Spaces ◽  
Orthonormal Bases

scholarly journals Orthonormal bases for α-modulation spaces

2010 ◽  
Vol 61 (2) ◽  
pp. 173-190 ◽  
Author(s):  
Morten Nielsen
Keyword(s):  
Modulation Spaces ◽  
Orthonormal Bases

Solving a linear fractional equation with nonlocal boundary conditions based on multiscale orthonormal bases method in the reproducing kernel space

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Wei Jiang ◽  
Zhong Chen ◽  
Ning Hu ◽  
Yali Chen
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Reproducing Kernel ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Kernel Space ◽  
Reproducing Kernel Space ◽  
Orthonormal Bases ◽  
Fractional Differential

AbstractIn recent years, the study of fractional differential equations has become a hot spot. It is more difficult to solve fractional differential equations with nonlocal boundary conditions. In this article, we propose a multiscale orthonormal bases collocation method for linear fractional-order nonlocal boundary value problems. In algorithm construction, the solution is expanded by the multiscale orthonormal bases of a reproducing kernel space. The nonlocal boundary conditions are transformed into operator equations, which are involved in finding the collocation coefficients as constrain conditions. In theory, the convergent order and stability analysis of the proposed method are presented rigorously. Finally, numerical examples show the stability, accuracy and effectiveness of the method.

Modified Wilson Orthonormal Bases

2007 ◽  
Vol 6 (2) ◽  
pp. 223-235
Author(s):  
Piotr Wojdyłło
Keyword(s):  
Orthonormal Bases

scholarly journals Shear madness: new orthonormal bases and frames using chirp functions

1993 ◽  
Vol 41 (12) ◽  
pp. 3543-3549 ◽  
Author(s):  
R.G. Baraniuk ◽  
D.L. Jones
Keyword(s):  
Orthonormal Bases

scholarly journals Hermite Functions and Fourier Series

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 853
Author(s):  
Enrico Celeghini ◽  
Manuel Gadella ◽  
Mariano del Olmo
Keyword(s):  
Fourier Transform ◽  
Hermite Functions ◽  
Quantum Oscillator ◽  
Linear Combinations ◽  
Ladder Operators ◽  
Orthonormal Bases ◽  
Integrable Functions ◽  
The Fourier Transform ◽  
The One ◽  
Square Integrable Functions

Using normalized Hermite functions, we construct bases in the space of square integrable functions on the unit circle (L2(C)) and in l2(Z), which are related to each other by means of the Fourier transform and the discrete Fourier transform. These relations are unitary. The construction of orthonormal bases requires the use of the Gramm–Schmidt method. On both spaces, we have provided ladder operators with the same properties as the ladder operators for the one-dimensional quantum oscillator. These operators are linear combinations of some multiplication- and differentiation-like operators that, when applied to periodic functions, preserve periodicity. Finally, we have constructed riggings for both L2(C) and l2(Z), so that all the mentioned operators are continuous.

scholarly journals Schatten p-class property of pseudodifferential operators with symbols in modulation spaces

2012 ◽  
Vol 205 ◽  
pp. 119-148
Author(s):  
Masaharu Kobayashi ◽  
Akihiko Miyachi
Keyword(s):  
Pseudodifferential Operators ◽  
Modulation Spaces

AbstractIt is proved that the pseudodifferential operators σt(X, D) belong to the Schatten p-class Cp, 0 < p ≤ 2, if the symbol σ(x,ω) is in certain modulation spaces on

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