scholarly journals On an infinite convolution product of measures

2001 ◽  
Vol 77 (1) ◽  
pp. 20-21
Author(s):  
Motoo Uchida
Keyword(s):  
Convolution Product ◽  
Infinite Convolution

scholarly journals THE SMOOTHNESS OF ORBITAL MEASURES ON NONCOMPACT SYMMETRIC SPACES

2021 ◽  
pp. 1-20
Author(s):  
SANJIV KUMAR GUPTA ◽  
KATHRYN E. HARE
Keyword(s):  
Symmetric Space ◽  
Symmetric Spaces ◽  
Continuous Measure ◽  
Convolution Product ◽  
Absolutely Continuous ◽  
Regular Elements ◽  
Connected Subgroup ◽  
Decay Properties ◽  
Absolutely Continuous Measure ◽  
Special Case

Abstract Let $G/K$ be an irreducible symmetric space, where G is a noncompact, connected Lie group and K is a compact, connected subgroup. We use decay properties of the spherical functions to show that the convolution product of any $r=r(G/K)$ continuous orbital measures has its density function in $L^{2}(G)$ and hence is an absolutely continuous measure with respect to the Haar measure. The number r is approximately the rank of $G/K$ . For the special case of the orbital measures, $\nu _{a_{i}}$ , supported on the double cosets $Ka_{i}K$ , where $a_{i}$ belongs to the dense set of regular elements, we prove the sharp result that $\nu _{a_{1}}\ast \nu _{a_{2}}\in L^{2},$ except for the symmetric space of Cartan class $AI$ when the convolution of three orbital measures is needed (even though $\nu _{a_{1}}\ast \nu _{a_{2}}$ is absolutely continuous).

scholarly journals Gauge × gauge = gravity on homogeneous spaces using tensor convolutions

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
L. Borsten ◽  
I. Jubb ◽  
V. Makwana ◽  
S. Nagy
Keyword(s):  
Homogeneous Spaces ◽  
Gauge Fields ◽  
Convolution Product ◽  
Tensor Fields ◽  
Einstein Universe ◽  
Gauge Transformations ◽  
Yang Mills ◽  
Static Einstein Universe ◽  
Definition Of ◽  
Gauge Gravity

Abstract A definition of a convolution of tensor fields on group manifolds is given, which is then generalised to generic homogeneous spaces. This is applied to the product of gauge fields in the context of ‘gravity = gauge × gauge’. In particular, it is shown that the linear Becchi-Rouet-Stora-Tyutin (BRST) gauge transformations of two Yang-Mills gauge fields generate the linear BRST diffeomorphism transformations of the graviton. This facilitates the definition of the ‘gauge × gauge’ convolution product on, for example, the static Einstein universe, and more generally for ultrastatic spacetimes with compact spatial slices.

scholarly journals One dimensional fractional frequency Sumudu transform by inverse α−difference operator

10.26524/cm73 ◽  
2020 ◽  
Vol 4 (1) ◽  
Author(s):  
Chandrasekar B ◽  
Meganathan M ◽  
Vasuki S
Keyword(s):  
Difference Operator ◽  
Convolution Product ◽  
One Dimensional ◽  
Fractional Frequency ◽  
Sumudu Transform

In this paper, we define fractional frequency Sumudu transform by inverse α−difference operator. Here we present certain new results on Sumudu transform of polynomial factorial,trigonometric and geometric functions using shift value. Finally, we provide the relation between convolution product and fractional Sumudu transform of polynomial and exponential function.Numerical results are verified and analysed the outcomes by graphs.

scholarly journals Spaces ofDLptype and a convolution product associated with the spherical mean operator

2005 ◽  
Vol 2005 (3) ◽  
pp. 357-381 ◽  
Author(s):  
M. Dziri ◽  
M. Jelassi ◽  
L. T. Rachdi
Keyword(s):  
Harmonic Analysis ◽  
Dual Space ◽  
Convolution Product ◽  
Spherical Mean Operator ◽  
Spherical Mean

We define and study the spacesℳp(ℝ×ℝn),1≤p≤∞, that are ofDLptype. Using the harmonic analysis associated with the spherical mean operator, we give a new characterization of the dual spaceℳ′p(ℝ×ℝn)and describe its bounded subsets. Next, we define a convolution product inℳ′p(ℝ×ℝn)×Mr(ℝ×ℝn),1≤r≤p<∞, and prove some new results.

THE FOURIER-JACOBI WAVELET CONVOLUTION PRODUCT

2021 ◽  
Vol 10 (4) ◽  
pp. 2255-2267
Author(s):  
C. P. Pandey ◽  
P. Phukan ◽  
M. Ado
Keyword(s):  
Wavelet Transformation ◽  
Convolution Product ◽  
Norm Inequalities

The convolution product associated with the Fourier-Jacobi wavelet transformation is investigated. Certain norm inequalities for the convolution product are established.

Sign in / Sign up

Export Citation Format

Share Document