• Corpus ID: 234742069

B-splines on the Heisenberg group

@inproceedings{Das2021BsplinesOT,
  title={B-splines on the Heisenberg group},
  author={Santi Rani Das and Peter R. Massopust and Radha Ramakrishnan},
  year={2021}
}
In this paper, we introduce a class of B-splines on the Heisenberg group H and study their fundamental properties. Unlike the classical case, we prove that there does not exist any sequence {αn}n∈N such that L(−n.−n 2 ,−αn)φn(x, y, t) = L(−n.−2 ,−αn)φn(−x,−y,−t), for n ≥ 2, where L(x,y,t) denotes the left translation on H. We further investigate the problem of finding an equivalent condition for the system of left translates to form a frame sequence or a Riesz sequence in terms of twisted… 

References

SHOWING 1-10 OF 22 REFERENCES

Shift-invariant Spaces with Countably Many Mutually Orthogonal Generators on the Heisenberg group

Let $E(\mathscr{A})$ denote the shift-invariant space associated with a countable family $\mathscr{A}$ of functions in $L^{2}(\mathbb{H}^{n})$ with mutually orthogonal generators, where

Riesz sequences of translates and generalized duals with support on [0, 1]

If the integer translates of a function ø with compact support generate a frame for a subspace W of L2(ℝ),then it is automatically a Riesz basis for W, and there exists a unique dual Riesz basis

Reproducing formulas for generalized translation invariant systems on locally compact abelian groups

In this paper we connect the well established discrete frame theory of generalized shift invariant systems to a continuous frame theory. To do so, we let j, j 2 J, be a countable family of closed,

Frames generated by compact group actions

Let $K$ be a compact group, and let $\rho$ be a representation of $K$ on a Hilbert space $\mathcal{H}_\rho$. We classify invariant subspaces of $\mathcal{H}_\rho$ in terms of range functions, and

Twisted B-splines in the complex plane

Orthonormality of wavelet system on the Heisenberg group

Shift-invariant system on the Heisenberg Group

In this paper, a shift-invariant system of the form $$\{L_{a\nu }g_s:\nu \in \varGamma ,s\in {{\mathbb {Z}}}\}$$ for $$a>0$$ is studied on the Heisenberg group $${{\mathbb {H}}^n}$$ , where

Interpolation and Approximation with Splines and Fractals

This textbook is intended to supplement the classical theory of uni- and multivariate splines and their approximation and interpolation properties with those of fractals, fractal functions, and