The Trace Formula for the Heat Semigroup with Polynomial Potential

2011 ◽  
pp. 3-21 ◽  
Author(s):  
Sergio Albeverio ◽  
Sonia Mazzucchi
Keyword(s):  
Trace Formula ◽  
Heat Semigroup ◽  
Polynomial Potential

scholarly journals Heat kernels of the discrete Laguerre operators

2021 ◽  
Vol 111 (2) ◽  
Author(s):  
Aleksey Kostenko
Keyword(s):  
Hardy Inequality ◽  
Jacobi Polynomials ◽  
Heat Kernels ◽  
The Other ◽  
Heat Semigroup ◽  
Stochastic Completeness ◽  
Markovian Semigroup ◽  
Other Hand ◽  
The One

AbstractFor the discrete Laguerre operators we compute explicitly the corresponding heat kernels by expressing them with the help of Jacobi polynomials. This enables us to show that the heat semigroup is ultracontractive and to compute the corresponding norms. On the one hand, this helps us to answer basic questions (recurrence, stochastic completeness) regarding the associated Markovian semigroup. On the other hand, we prove the analogs of the Cwiekel–Lieb–Rosenblum and the Bargmann estimates for perturbations of the Laguerre operators, as well as the optimal Hardy inequality.

The Helton-Howe trace formula for submodules

2021 ◽  
pp. 108997
Author(s):  
Quanlei Fang ◽  
Yi Wang ◽  
Jingbo Xia
Keyword(s):  
Trace Formula

scholarly journals A Selberg trace formula for hypercomplex analytic cusp forms

2015 ◽  
Vol 148 ◽  
pp. 398-428 ◽  
Author(s):  
D. Grob ◽  
R.S. Kraußhar
Keyword(s):  
Trace Formula ◽  
Cusp Forms ◽  
Selberg Trace Formula

scholarly journals A trace formula for vector-valued modular forms

2015 ◽  
Vol 17 (06) ◽  
pp. 1550069
Author(s):  
P. Bantay
Keyword(s):  
Trace Formula ◽  
Modular Forms ◽  
Weight Distribution ◽  
Hilbert Polynomial ◽  
Free Generators ◽  
Vector Valued

We present a formula for vector-valued modular forms, expressing the value of the Hilbert-polynomial of the module of holomorphic forms evaluated at specific arguments in terms of traces of representation matrices, restricting the weight distribution of the free generators.

Closed-Form Expression for the Exact Period of a Nonlinear Oscillator Typified by a Mass Attached to a Stretched Wire

2011 ◽  
Vol 3 (6) ◽  
pp. 689-701
Author(s):  
Malik Mamode
Keyword(s):  
Harmonic Balance ◽  
Nonlinear Oscillator ◽  
Harmonic Balance Method ◽  
Elliptic Functions ◽  
Oscillatory System ◽  
Balance Method ◽  
Closed Form Expression ◽  
Form Expression ◽  
Polynomial Potential ◽  
Exact Analytical Expression

AbstractThe exact analytical expression of the period of a conservative nonlinear oscillator with a non-polynomial potential, is obtained. Such an oscillatory system corresponds to the transverse vibration of a particle attached to the center of a stretched elastic wire. The result is given in terms of elliptic functions and validates the approximate formulae derived from various approximation procedures as the harmonic balance method and the rational harmonic balance method usually implemented for solving such a nonlinear problem.

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