Integrable operator representations of ℝ q 2 ,X q,γ andSL q (2, ℝ)

1994 ◽  
Vol 159 (2) ◽  
pp. 217-237 ◽  
Author(s):  
Konrad Schmüdgen
Keyword(s):  
Integrable Operator ◽  
Operator Representations

scholarly journals On Approximate Operator Representations of Sequences in Banach Spaces

2021 ◽  
Vol 15 (3) ◽  
Author(s):  
Ole Christensen ◽  
Marzieh Hasannasab ◽  
Gabriele Steidl
Keyword(s):  
Banach Spaces ◽  
Operator Representations

scholarly journals Operator Representation of Fermi-Dirac and Bose-Einstein Integral Functions with Applications

2007 ◽  
Vol 2007 ◽  
pp. 1-9 ◽  
Author(s):  
M. Aslam Chaudhry ◽  
Asghar Qadir
Keyword(s):  
Zeta Function ◽  
Riemann Zeta Function ◽  
Statistical Distributions ◽  
Operator Representation ◽  
The Riemann Zeta Function ◽  
Riemann Zeta ◽  
Quantum Statistical ◽  
Bose Einstein ◽  
Operator Representations ◽  
Class Of Functions

Fermi-Dirac and Bose-Einstein functions arise as quantum statistical distributions. The Riemann zeta function and its extension, the polylogarithm function, arise in the theory of numbers. Though it might not have been expected, these two sets of functions belong to a wider class of functions whose members have operator representations. In particular, we show that the Fermi-Dirac and Bose-Einstein integral functions are expressible as operator representations in terms of themselves. Simpler derivations of previously known results of these functions are obtained by their operator representations.

scholarly journals Well-behaved unbounded operator representations and unbounded $C^*$ -seminorms

2004 ◽  
Vol 56 (2) ◽  
pp. 417-445 ◽  
Author(s):  
Subhash J. BHATT ◽  
Atsushi INOUE ◽  
Klaus-Detlef KÜRSTEN
Keyword(s):  
Unbounded Operator ◽  
Operator Representations

scholarly journals Fourier transform from momentum space to twistor space

2020 ◽  
pp. 2150032
Author(s):  
Jun-ichi Note
Keyword(s):  
Fourier Transform ◽  
Momentum Space ◽  
Twistor Space ◽  
Three Dimensional ◽  
Yang Mills ◽  
The Fourier Transform ◽  
Complex Integral ◽  
Cech Cohomology ◽  
Complex Projective ◽  
Operator Representations

Several methods use the Fourier transform from momentum space to twistor space to analyze scattering amplitudes in Yang–Mills theory. However, the transform has not been defined as a concrete complex integral when the twistor space is a three-dimensional complex projective space. To the best of our knowledge, this is the first study to define it as well as its inverse in terms of a concrete complex integral. In addition, our study is the first to show that the Fourier transform is an isomorphism from the zeroth Čech cohomology group to the first one. Moreover, the well-known twistor operator representations in twistor theory literature are shown to be valid for the Fourier transform and its inverse transform. Finally, we identify functions over which the application of the operators is closed.

Operator representations of U q (sl2(?))

1996 ◽  
Vol 37 (2) ◽  
pp. 211-222 ◽  
Author(s):  
Konrad Schm�dgen
Keyword(s):  
Operator Representations

Representations of E7, equivalent combinatorics and algebraic varieties

2018 ◽  
Vol 17 (03) ◽  
pp. 1850045
Author(s):  
Xiaoping Xu
Keyword(s):  
Order Differential Operator ◽  
Moody Algebra ◽  
Oscillator Representation ◽  
Bosonic Field ◽  
Space Forms ◽  
Combinatorial Properties ◽  
First Order ◽  
Vector Formula ◽  
Operator Representations ◽  
Dimensional Module

In our earlier work on a new functor from [Formula: see text]-Mod to [Formula: see text]-Mod, we found a one-parameter ([Formula: see text]) family of inhomogeneous first-order differential operator representations of the simple Lie algebra of type [Formula: see text] in [Formula: see text] variables. Letting these operators act on the space of exponential-polynomial functions that depend on a parametric vector [Formula: see text], we prove that the space forms an irreducible [Formula: see text]-module for any [Formula: see text] if [Formula: see text] is not on an explicitly given projective algebraic variety. Certain equivalent combinatorial properties of the basic oscillator representation of [Formula: see text] over its 27-dimensional module play key roles in our proof. Our result can also be used to study free bosonic field irreducible representations of the corresponding affine Kac–Moody algebra.

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