Oscillatory Integrals and Edge Analysis of the Continuous Shearlet Transform

2013 ◽  
Vol 12 (2-3) ◽  
pp. 189-213
Author(s):  
Congwei Song
Keyword(s):  
Oscillatory Integrals ◽  
Shearlet Transform

Image de-noising algorithm based on Shearlet transform

2010 ◽  
Vol 30 (6) ◽  
pp. 1562-1564 ◽  
Author(s):  
Hai-zhi HU ◽  
Hui SUN ◽  
Cheng-zhi DENG ◽  
Xi CHEN ◽  
Zhi-hua LIU ◽  
...  
Keyword(s):  
Shearlet Transform

Local Spatio-Temporal Representation Using the 3D Shearlet Transform

2018 ◽  
Vol 17 (1) ◽  
pp. 57-72
Author(s):  
Damiano Malafronte ◽  
Ernesto De Vito ◽  
Francesca Odone
Keyword(s):  
Shearlet Transform ◽  
Temporal Representation ◽  
Spatio Temporal

scholarly journals Multidimensional van der Corput-Type estimates involving Mittag-Leffler functions

2020 ◽  
Vol 23 (6) ◽  
pp. 1663-1677
Author(s):  
Michael Ruzhansky ◽  
Berikbol T. Torebek
Keyword(s):  
Cauchy Problem ◽  
Exponential Function ◽  
Evolution Equations ◽  
Oscillatory Integrals ◽  
Schrödinger Equations ◽  
Fractional Evolution Equations ◽  
Type Function ◽  
Fractional Schrödinger Equations ◽  
The Cauchy Problem ◽  
Klein Gordon

Abstract The paper is devoted to study multidimensional van der Corput-type estimates for the intergrals involving Mittag-Leffler functions. The generalisation is that we replace the exponential function with the Mittag-Leffler-type function, to study multidimensional oscillatory integrals appearing in the analysis of time-fractional evolution equations. More specifically, we study two types of integrals with functions E α, β (i λ ϕ(x)), x ∈ ℝ N and E α, β (i α λ ϕ(x)), x ∈ ℝ N for the various range of α and β. Several generalisations of the van der Corput-type estimates are proved. As an application of the above results, the Cauchy problem for the multidimensional time-fractional Klein-Gordon and time-fractional Schrödinger equations are considered.

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