International Journal of Pure and Applied Mathematics Volume 116 No. 1 2017, 91-96 ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version) url: http://www.ijpam.eu doi: 10.12732/ijpam.v116i1.8 P A ijpam.eu LINEAR CANONICAL TRANSFORM FOR INTEGRABLE BOEHMIANS Pravinkumar V. Dole 1 § , S.K. Panchal 2 Department of Mathematics Dr. Babasaheb Ambedkar Marathwada University Aurangabad, 431004 (M.S.), INDIA Abstract: In this paper we extend the linear canonical transform to class of integrable Boehmians by using new definition of convolution defined in [3]. Further, we prove that the extended linear canonical transform have expected properties like linear, one-to-one, onto and continuous from one Boehmian space to another Boehmian space and obtained some basic properties. AMS Subject Classification: 44A35, 44A40, 46F12, 46F99 Key Words: linear canonical transform, generalized functions, convolutions, boehmians 1. Introduction Boehmian is a new class of generalized functions introduced by Boehme [1] which open the new door to area of research in mathematics [4, 5, 7, 8]. The construction of Boehmians is given by Mikusinski and Mikusinski. Mikusin- ski has studied Fourier transform of integrable Boehmians in [6]. Zayed and Abhishek singh extend the fractional Fourier transform to class of integrable Boehmians in [11, 9] respectively. Bhosale and Chaudhary [2] extended the fractional Fourier transform to distributions of compact support. The Fourier transform and fractional Fourier transform are the special cases of linear canoni- cal transform (LCT)[3]. Let L 1 (R) be the space of all complex valued absolutely integrable functions on R with norm ||f || 1 =  R |f (t)|dt ≤ M , for some M> 0. Received: February 24, 2017 Revised: June 21, 2017 Published: August 29, 2017 c  2017 Academic Publications, Ltd. url: www.acadpubl.eu § Correspondence author