We present the first results of a systematic search for the rare extragalactic radio sources showing an inverted ( integrated ) spectrum , with spectral index \alpha \geq + 2.0 , a previously unexplored spectral domain .
The search is expected to yield strong candidates for \alpha \geq + 2.5 , for which the standard synchrotron self-absorption ( characterized by a single power-law energy distribution of relativistic electron population ) would not be a plausible explanation , even in an ideal case of a perfectly homogeneous source of incoherent synchrotron radiation .
Such sharply inverted spectra , if found , would require alternative explanations , e.g. , free-free absorption , or non-standard energy distribution of relativistic electrons which differs from a power-law ( e.g. , Maxwellian ) .

The search was carried out by comparing two sensitive low-frequency radio surveys made with sub-arcminute resolution , namely , the WISH survey at 352 MHz and TGSS/DR5 at 150 MHz .
The overlap region between these two surveys contains 7056 WISH sources classified as ‘ single ’ and brighter than 100 mJy at 352 MHz .
We focus here on the seven of these sources for which we find \alpha > +2.0 .
Two of these are undetected at 150 MHz and are particularly good candidates for \alpha > +2.5 .
Five of the seven sources exhibit a ‘ Gigahertz-Peaked-Spectrum ’ ( GPS ) .