Inversion Formulas for the Lemniscate and Allied Functions

1994 ◽  
pp. 245-260
Author(s):  
Bruce C. Berndt
Keyword(s):  
Inversion Formulas

Erdélyi–Kober fractional integrals and radon transforms for mutually orthogonal affine planes

2020 ◽  
Vol 23 (4) ◽  
pp. 967-979
Author(s):  
Boris Rubin ◽  
Yingzhan Wang
Keyword(s):  
Fractional Integrals ◽  
Radon Transforms ◽  
Affine Planes ◽  
Inversion Formulas ◽  
Radial Functions ◽  
Compactly Supported ◽  
Radial Case ◽  
Compactly Supported Functions

AbstractWe apply Erdélyi–Kober fractional integrals to the study of Radon type transforms that take functions on the Grassmannian of j-dimensional affine planes in ℝn to functions on a similar manifold of k-dimensional planes by integration over the set of all j-planes that meet a given k-plane at a right angle. We obtain explicit inversion formulas for these transforms in the class of radial functions under minimal assumptions for all admissible dimensions. The general (not necessarily radial) case, but for j + k = n − 1, n odd, was studied by S. Helgason [8] and F. Gonzalez [4, 5] on smooth compactly supported functions.

scholarly journals Lagrange Inversion and Combinatorial Species with Uncountable Color Palette

2021 ◽  
Author(s):  
Sabine Jansen ◽  
Tobias Kuna ◽  
Dimitrios Tsagkarogiannis
Keyword(s):  
Lagrange Inversion ◽  
Inversion Formulas ◽  
Color Palette

AbstractWe prove a multivariate Lagrange-Good formula for functionals of uncountably many variables and investigate its relation with inversion formulas using trees. We clarify the cancellations that take place between the two aforementioned formulas and draw connections with similar approaches in a range of applications.

Inversion formulas for cone transforms arising in application of Compton cameras

2015 ◽  
Vol 31 (1) ◽  
pp. 015006 ◽  
Author(s):  
Chang-Yeol Jung ◽  
Sunghwan Moon
Keyword(s):  
Inversion Formulas

CERTAIN ISOMETRIES RELATED TO THE BILATERAL LAPLACE TRANSFORM

2006 ◽  
Vol 11 (3) ◽  
pp. 331-346 ◽  
Author(s):  
S. B. Yakubovich
Keyword(s):  
Hilbert Space ◽  
Entire Function ◽  
Laplace Transform ◽  
Hilbert Spaces ◽  
Reproducing Kernel ◽  
Reproducing Kernel Hilbert Space ◽  
Inversion Formulas ◽  
Mean Convergence ◽  
The Laplace Transform ◽  
The Mean

We study certain isometries between Hilbert spaces, which are generated by the bilateral Laplace transform In particular, we construct an analog of the Bargmann‐Fock type reproducing kernel Hilbert space related to this transformation. It is shown that under some integra‐bility conditions on $ the Laplace transform FF(z), z = x + iy is an entire function belonging to this space. The corresponding isometrical identities, representations of norms, analogs of the Paley‐Wiener and Plancherel's theorems are established. As an application this approach drives us to a different type of real inversion formulas for the bilateral Laplace transform in the mean convergence sense.

Some aspects of strong inversion formulas of an SFT

2018 ◽  
Vol 35 (1) ◽  
pp. 373-390 ◽  
Author(s):  
Shigeyoshi Ogawa ◽  
Hideaki Uemura
Keyword(s):  
Inversion Formulas ◽  
Strong Inversion
Sign in / Sign up

Export Citation Format

Share Document