scholarly journals An Integrability Theorem on Unbounded Vilenkin Groups

1993 ◽  
Vol 175 (2) ◽  
pp. 438-447 ◽  
Author(s):  
M. Avdispahic ◽  
M. Pepic
Keyword(s):  
Integrability Theorem ◽  
Vilenkin Groups

Autonomous Geometrical Mechanics

2018 ◽  
Author(s):  
Peter Mann
Keyword(s):  
Phase Space ◽  
Contact Structure ◽  
Invariant Tori ◽  
Time Dependent ◽  
Contact Structures ◽  
Natural Setting ◽  
Adiabatic Invariance ◽  
Jet Bundle ◽  
Integrability Theorem ◽  
Extended Phase

This chapter examines the structure of the phase space of an integrable system as being constructed from invariant tori using the Arnold–Liouville integrability theorem, and periodic flow and ergodic flow are investigated using action-angle theory. Time-dependent mechanics is formulated by extending the symplectic structure to a contact structure in an extended phase space before it is shown that mechanics has a natural setting on a jet bundle. The chapter then describes phase space of integrable systems and how tori behave when time-dependent dynamics occurs. Adiabatic invariance is discussed, as well as slow and fast Hamiltonian systems, the Hannay angle and counter adiabatic terms. In addition, the chapter discusses foliation, resonant tori, non-resonant tori, contact structures, Pfaffian forms, jet manifolds and Stokes’s theorem.

scholarly journals Multiresolution analysis and wavelets on Vilenkin groups

2008 ◽  
Vol 21 (3) ◽  
pp. 309-325 ◽  
Author(s):  
Yury Farkov
Keyword(s):  
Multiresolution Analysis ◽  
Linear Independence ◽  
Sufficient Conditions ◽  
Partition Of Unity ◽  
Necessary And Sufficient Conditions ◽  
Refinable Functions ◽  
Vilenkin Groups ◽  
Orthogonal Wavelets ◽  
The Stability ◽  
Necessary And Sufficient

This paper gives a review of multiresolution analysis and compactly sup- ported orthogonal wavelets on Vilenkin groups. The Strang-Fix condition, the partition of unity property, the linear independence, the stability, and the orthonormality of 'integer shifts' of the corresponding refinable functions are considered. Necessary and sufficient conditions are given for refinable functions to generate a multiresolution analysis in the L2-spaces on Vilenkin groups. Several examples are provided to illustrate these results. .

Convergence of Marcinkiewicz Means of Integrable Functions with Respect to Two-Dimensional Vilenkin Systems

2004 ◽  
Vol 11 (3) ◽  
pp. 467-478
Author(s):  
György Gát
Keyword(s):  
Maximal Operator ◽  
Weak Type ◽  
Integrable Function ◽  
Two Dimensional ◽  
Vilenkin Groups ◽  
Almost Everywhere ◽  
Integrable Functions ◽  
Marcinkiewicz Means

Abstract We prove that the maximal operator of the Marcinkiewicz mean of integrable two-variable functions is of weak type (1, 1) on bounded two-dimensional Vilenkin groups. Moreover, for any integrable function 𝑓 the Marcinkiewicz mean σ 𝑛𝑓 converges to 𝑓 almost everywhere.

The Euler-Jacobi-Lie integrability theorem

2013 ◽  
Vol 18 (4) ◽  
pp. 329-343 ◽  
Author(s):  
Valery V. Kozlov
Keyword(s):  
Integrability Theorem
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