Question: "In the Verse 11.14.35 of "Shreemad Bhagavatam" Lord Shree Krishna says about Pranayama with OM (Pranava, Omkara). Where I can find more elaborate instructions on Pranayama within Vaishnava Parivara?".
Answer by Vishnudut1926: "Actually Pranayama practice is better to be received from Tantrik Vaishnava Guru along with Bhuta-Shuddhi, Nyasas and other Upangas, because wrongly implemented Pranayama can just kill an upasaka.
And in "Shreemad-Bhagavatam" Bhagavan Shree Krishna just
gives preliminary Pranayama-Upadesha (Pranayama-Instructions) hoping that the further instructions will be received from Vaishnava-Guru.
Anyway, one of the most elaborate Pranayama upadesha (instructions) can be found in "Shree Krama-Dipika".
In "Shree Krama-Dipika" it is recommended to use Tantrik Bijas during Pranayama (not AUM, but for example KLIM - the Tantrik Bija of Shreemati Radharani-Devi and Bhagavan Shree Krishna).
Question: "Why Bhagavan Shree Krishna did not tell about KLIM-Pranayama in "Shreemad-Bhagavatam"?
Answer by Vishnudut1926: "Because "Shreemad Bhagavatam" is not a Vaishnava-Tantra (though "Shreemad Bhagavatam" do has some Tantrik Khandas - for example, "Shree Narayana-Kavacham").
Anyway, Lord Shree Krishna always writes more elaborate instructions in Vaishnava Tantras and Agamas. As for Shree Gaudiya-Sampradaya, as far as I remember they have a separate sub-chapter devoted to Vaishnava-Pranayama in "Shree Hari-Bhakti-Vilasa" - a kind of Tantrik/Puranic Paddhati compiled by OM VishnuPad Shrila Sanatana Goswami for Gaudiya-Vaishnavas.
However, please don't hesitate to study "Shree Krama-Dipika" in Hindi too, this is very loveable and wonderful Shree Krishna-Tantra.
And the Verse 11.14.35 of "Shreemad Bhagavatam" is very beautiful, Bhagavan Shree Krishna promises Pranayama-Siddhi just within a month in this verse (providing an upasaka follows the right methodology):
एवं प्रणव-संयुक्तं प्राणम् एव समभ्यसेत्दश-कृत्वस् त्रि-षवणं मासाद् अर्वाग् जितानिलः
"Being fixed in the oṁkāra, one should carefully practice the prāṇāyāma system ten times at each sunrise, noon and sunset. Thus, after one month one will have conquered the life air".
