This is a partial answer, as I've traced this back far enough to find significant connections to pseudo-science and basis for doubt, but I haven't found any sources that directly refute the claims, e.g. through experimental trials.
This stuff appears to be pushed by Anthony Holland, who's started an organization called Novobiotronics. Holland describes their work as continuing from widely rejected research from the 1930's. At this time, there doesn't appear to be much mainstream acceptance.
The main guy behind this appears to be Anthony Holland. No Wikipedia page, but apparently he's an "Associate Professor of Music" at Skidmore College, as alluded to in his YouTube video in which he notes that he's a "music professor".
According to Holland's CV, he got his PhD in "Musical Arts" in 1982 from "Cleveland Institute of Music (Composition) and Case Western Reserve University, Cleveland, Ohio" (presumably the Cleveland Institute of Music).
I point this out for two reasons:
It seems unlikely that someone who has no apparent formal education in science, let alone medicine, would be prepared to understand the nature of their own claims.
Throughout much of his website and press, he uses the "Dr." title and claims to be a "PhD", which strikes me as very misleading.
Anyway, apparently he's started a non-profit organization called Novobiotronics, apparently with support from a GoFundMe campaign that claims 6,500 USD in donations. From that GoFundMe:
We are a nonprofit small grass roots research company that has developed a way of killing up to 60% of cancer cells (in laboratory experiments) without using any drugs (no chemo!) or radiation (no radiation!). We believe our research will lead to a future cancer treatment that is nontoxic (no side effects!), noninvasive (no needles or surgery!) and inexpensive.
The new treatment is electronic: frequency-specific pulsed electric feilds[sic] are directed at cancer cells using a special 'plasma antenna' (something like a special fluorescent light....which broadcasts powerful electric fields which kill cancer cells and slows their growth rate also).
—"Novobiotronics Shattering Cancer", GoFundMe
Holland refers to their technology as "pulse magnetotherapy (PEMF)"; Wikipedia lists this as a synonym for "pulsed electromagnetic field therapy (PEMFT)".
RE: "Is this research based on anything?"
According to Holland, these claims follow from earlier work by Royal Rife:
Our company was the first to produce documented research in a major cancer research lab using a Rife type device (Rife-Bare plasma device).
Dear Yves, I've done considerable research on Roy Rife. While I greatly admire all that he accomplished, he never was able to document the affects of his machine in vitro in laboratory experiments (or if he was, that material has been lost to history), and his famous cancer treatments of the early 1930's.....there is no extant medical documentation on that whatsoever (if you find some, send me the link please). Unfortunately, according to Rife himself, all those records were 'lost'.
Our company is the first to document the affects of Oscillating Pulsed Electric Fields (OPEF) as broadcast by an enclosed gas plasma antenna against cancer cells in vitro and against antibiotic resistant bacteria (MRSA and pseudomonas).
We are not taking credit for Rife's work, rather we are taking the time to fully document it in modern day laboratory experiments. The website links we sent include some of the best documentation to date.
—Anthony Holland in "Is there someone who has experience in using the Rife frequency generator for cancer treatment?", ResearchGate
Here's Wikipedia's description of the earlier researcher, Rife:
Royal Raymond Rife (May 16, 1888 – August 5, 1971) was an American inventor and early exponent of high-magnification time-lapse cine-micrography. In the 1930s, he claimed that by using a specially designed optical microscope, he could observe microbes which were too small to visualize with previously existing technology. Rife also reported that a 'beam ray' device of his invention could weaken or destroy the pathogens by energetically exciting destructive resonances in their constituent chemicals.
—"Royal Rife", Wikipedia [links and citations omitted]
Holland also considers a more recent line of work, on Novocure, to have set the stage for his efforts:
One particular scientific behemoth known as Novocure is serving as the giant ice-breaking, boundary destroying ship currently plying the waters of mainstream American medicine.
Novocure has already had their electronic treatment for brain cancer (recurring glioblastoma) approved by the FDA and has moved aggressively throughout the country in establishing both treatment centers and patient financing plans, since the treatment is not yet covered by American medical insurance companies (one doctor friend of mine informs me that they lease their device for $15,000/month, a sum that very few Americans can afford). While American insurance companies continue to hold a hard line on covering the cost of electronic treatments for cancer, some do cover the use of some electronic devices, TENS for example, for chronic pain treatment.
—Anthony Holland in "Electronic Frequency Treatment in Mainstreet USA"
Update: TEDx has flagged the YouTube video.
The YouTube video of Holland's TEDx talk now has a disclaimer at the beginning of its description:
NOTE FROM TED: Please do not look to this talk for medical advice. We've flagged this talk, which was filmed at a TEDx event, because it appears to fall outside TEDx's content guidelines. Resonant Frequency Therapy has not been proven effective by scientific research. The guidelines we give TEDx organizers are described in more detail here
—"Shattering cancer with resonant frequencies: Anthony Holland at TEDxSkidmoreCollege", YouTube (2013-12-22) [link reformatted]