Recently A. Knapp [3] announced that every unitary principal series representation of a semisimple lie group decomposes simply; that is, no two distinct irreducible components of a given unitary principal series representation are equivalent. In proving this result Knapp analyzed in detail the structure of the spaces of intertwining operators for principal series representations. His analysis u...

One of the four well-known series of simple Lie algebras of Cartan type is the series of Lie algebras of Special type, which are divergence-free Lie algebras associated with polynomial algebras and the operators of taking partial derivatives, connected with volume-preserving diffeomorphisms. In this paper, we determine the structure space of the divergence-free Lie algebras associated with pair...

Conventional Fourier analysis has many schemes for different types of signals. They are Fourier transform (FT), Fourier series (FS), discrete-time Fourier transform (DTFT), and discrete Fourier transform (DFT). The goal of this correspondence is to develop two absent schemes of fractional Fourier analysis methods. The proposed methods are fractional Fourier series (FRFS) and discrete-time fract...

A novel technique of analysis of an arbitrary primary time series into a set of secondary, timelimited, local, constituent time series, the TT-transform, is presented. The time–time representation is derived from the S-transform, a method of representation of a real time series as a set of complex, time-localized spectra. When integrated over time, the S-transform becomes the Fourier transform ...

A known theorem, Nigam 2010 dealing with the degree of approximation of conjugate of a signal belonging to Lipξ t -class by E, 1 C, 1 product summability means of conjugate series of Fourier series has been generalized for the weighted W Lr, ξ t , r ≥ 1 , t > 0 -class, where ξ t is nonnegative and increasing function of t, by ̃ E1 nC n which is in more general form of Theorem 2 of Nigam and Shar...