The main objective of this paper is to study the composition of continuous Kontorovich-Lebedev wavelet transform (KL-wavelet transform) and wave packet transform (WPT) based on the Kontorovich-Lebedev transform (KL-transform). Estimates for KL-wavelet and KL-wavelet transform are obtained, and Plancherel?s relation for composition of KL-wavelet transform and WPT-transform are derived. Reconstruction formula for WPT associated to KL-transform is also deduced and at the end Calderon?s formula related to KL-transform using its convolution property is obtained.

Mature embryos of einkorn (Triticum monococcum ssp. monococcum) and bread (Triticum aestivum) wheat were used for callus induction on media containing four (0, 1, 2 and 4 mg L− 1) different doses of 2,4-D and dicamba supplemented with under five (0, 6.2, 12.4, 24.8, and 37.2 mg L− 1) different boron stresses. The obtained callus was transferred to culture media with three (0, 0.5, and 2 mg L− 1) different BAP doses with five boron stresses for regeneration. The heaviest callus weight in einkorn wheat was in culture media with 1 mg L− 1 dicamba and 6.2 mg L− 1 (3.71 ± 0.13 g). Bread wheat had the heaviest callus weight on culture media with 4 mg L− 1 dicamba and 12.4 mg L− 1 (3.46 ± 0.40 g). Callus diameters were observed as the highest in culture media with 1 mg L− 1 and 12.4 mg L− 1 (1.10 ± 0.31) for einkorn and 4 mg L− 1 dicamba with 6.2 mg L− 1 boron (1.22 ± 0.27 cm) for bread wheat. Regeneration capacity was highest in control group with 6.2 mg L− 1 for both wheat genotypes (einkorn, 71.33% ± 11.78 and bread, 65.33% ± 10.80). The highest plantlet numbers were in only 2 mg L− 1 BAP (2.92 ± 0.88) for einkorn wheat and 0.5 mg L− 1 BAP supplemented with 6.2 mg L− 1 boron (3.71 ± 1.12) for bread wheat. This indirect regeneration protocol using mature embryos of einkorn and bread wheat under boron stresses may be useful for wheat breeding studies.