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The motivation of this article stems from the fact that weak solutions of some partial differential equations exist in a distributional sense, even when there are no strong solutions in spaces of continuous functions with the derivatives understood in the classical sense. For $$1\leqq p

With the help of linear canonical transform, we characterize a new class of pseudo-differential operators involving a general symbol \(\eta (x,y)\). Asymptotic series expansion of pseudo-differential operators associated with the general symbol is derived by using the theory of linear canonical transform.

In this article, we study the degree of convergence of Euler, Borel, and (e, c) transforms of the Fourier series of functions of class Lip(α, p), for p > 1. When p tends to infinity, the results yield known results in the supremum norm studied by P. Sadangi (Sadangi, Degree of Convergence of functions in the Holder metric, Ph.D. Thesis, Utkal University, 2006). The results of this chapter set the stage for further generalizations in other function spaces.