In this paper,we will discuss some properties of the(n,m)-spherical fuctions on the Lie group G=SL(2, R),and obtain the decomposition of f in C_c^4(G)into these functions.Also we give the Fourier inversion formula for...In this paper,we will discuss some properties of the(n,m)-spherical fuctions on the Lie group G=SL(2, R),and obtain the decomposition of f in C_c^4(G)into these functions.Also we give the Fourier inversion formula for the(n,m)-spherical functions in C_c^3(G).展开更多
In this paper, a better asymptotic order of Fourier transform on SL(2,R) is obtained by using classical analysis and Lie analysis comparing with that of [5],[6] ,and the Plancherel theorem on C2i(SL(2,R)) is also obta...In this paper, a better asymptotic order of Fourier transform on SL(2,R) is obtained by using classical analysis and Lie analysis comparing with that of [5],[6] ,and the Plancherel theorem on C2i(SL(2,R)) is also obtained as an application.展开更多
The key point of the method of calculating the normal form of ordinary differential equations based on the representation theory of sl (2, R) is to find generators of KerL_M and Kerad_M. In this paper, we give the nec...The key point of the method of calculating the normal form of ordinary differential equations based on the representation theory of sl (2, R) is to find generators of KerL_M and Kerad_M. In this paper, we give the necessary and sufficient conditions for generators of KerL_M and Ker ad_M and prove that any vector-valued polynomial in Ker ad_M can be constructed from polynomials in KerL_M in a certain way.展开更多
Algebraic solutions of the D-dimensional Schrodinger equation with Killingbeck potential are investigated using the Lie algebraic approach within the framework of quasi-exact solvability. The spectrum and wavefunction...Algebraic solutions of the D-dimensional Schrodinger equation with Killingbeck potential are investigated using the Lie algebraic approach within the framework of quasi-exact solvability. The spectrum and wavefunctions of the system are reported and the allowed values of the potential parameters are obtained through the sl（2） algebraization.展开更多
We introduce in this paper cryptographic protocols which use combinatorial group theory. Based on a combinatorial distribution of shares we present secret sharing schemes and cryptosystems using Nielsen transformation...We introduce in this paper cryptographic protocols which use combinatorial group theory. Based on a combinatorial distribution of shares we present secret sharing schemes and cryptosystems using Nielsen transformations. Nielsen transformations are a linear technique to study free groups and general infinite groups. In addition the group of all automorphisms of a free group F, denoted by AUT (F), is generated by a regular Nielsen transformation between two basis of F, and each regular Nielsen transformation between two basis of F defines an automorphism of F.展开更多
In this paper, we give the following dominated theorem: Let φ(g) ∈ L1(G//K),φε(t)=ε> 0, and the least radical decreasing dominatedfunction φ(t) = sup |φ(y)| ∈L1(G//K). If shtφ(t) is monotonically decreasin...In this paper, we give the following dominated theorem: Let φ(g) ∈ L1(G//K),φε(t)=ε> 0, and the least radical decreasing dominatedfunction φ(t) = sup |φ(y)| ∈L1(G//K). If shtφ(t) is monotonically decreasingon (0, ∞), then for any f∈L1loc(G//K) , the following inequality holds:sup |φε * f(x)| ≤ Cmf(x),where mf(x) is the Hardy-Littlewood maximal function of f, and C = ||φ||1.An application of this dominated theorem is also given.展开更多
文摘In this paper,we will discuss some properties of the(n,m)-spherical fuctions on the Lie group G=SL(2, R),and obtain the decomposition of f in C_c^4(G)into these functions.Also we give the Fourier inversion formula for the(n,m)-spherical functions in C_c^3(G).
文摘In this paper, a better asymptotic order of Fourier transform on SL(2,R) is obtained by using classical analysis and Lie analysis comparing with that of [5],[6] ,and the Plancherel theorem on C2i(SL(2,R)) is also obtained as an application.
基金Project supported by the National Natural Science Foundation of China.
文摘The key point of the method of calculating the normal form of ordinary differential equations based on the representation theory of sl (2, R) is to find generators of KerL_M and Kerad_M. In this paper, we give the necessary and sufficient conditions for generators of KerL_M and Ker ad_M and prove that any vector-valued polynomial in Ker ad_M can be constructed from polynomials in KerL_M in a certain way.
文摘Algebraic solutions of the D-dimensional Schrodinger equation with Killingbeck potential are investigated using the Lie algebraic approach within the framework of quasi-exact solvability. The spectrum and wavefunctions of the system are reported and the allowed values of the potential parameters are obtained through the sl（2） algebraization.
文摘We introduce in this paper cryptographic protocols which use combinatorial group theory. Based on a combinatorial distribution of shares we present secret sharing schemes and cryptosystems using Nielsen transformations. Nielsen transformations are a linear technique to study free groups and general infinite groups. In addition the group of all automorphisms of a free group F, denoted by AUT (F), is generated by a regular Nielsen transformation between two basis of F, and each regular Nielsen transformation between two basis of F defines an automorphism of F.
文摘In this paper, we give the following dominated theorem: Let φ(g) ∈ L1(G//K),φε(t)=ε> 0, and the least radical decreasing dominatedfunction φ(t) = sup |φ(y)| ∈L1(G//K). If shtφ(t) is monotonically decreasingon (0, ∞), then for any f∈L1loc(G//K) , the following inequality holds:sup |φε * f(x)| ≤ Cmf(x),where mf(x) is the Hardy-Littlewood maximal function of f, and C = ||φ||1.An application of this dominated theorem is also given.
