Revisiting the Fourier transform on the Heisenberg group

A recent theorem of S. Alesker, S. Artstein-Avidan and V. Milman characterises the Fourier transform on Rn as essentially the only transform on the space of tempered distributions which interchanges convolutions and pointwise products. In this note we study the image of the Schwartz space on the Heisenberg group under the Fourier transform and obtain a similar characterisation for the Fourier transform on the Heisenberg group

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Record landings of cephalopods by trawlers at Veraval during first quarter of 2009

Cephalopods represent one of the most important exploited marine fishery resources at Veraval. The cephalopod landings in Gujarat increased by more than two folds from 0.234 lakh t in 2002 to 0.49 lakh t in 2006 (Mohanraj et al., 2009), with a concomitant increase in catch rate from 5.05 kg h-1 in 2003 to 14.74 kg h-1 in 2006. The cephalopod resource was constituted mainly by Loligo duvauceli, Sepia pharaonis and S. aculeat

On heat equations associated with fractional harmonic oscillators

We establish some fixed-time decay estimates in Lebesgue spaces for the fractional heat propagator e−t Hβ , t,β > 0, associated with the harmonic oscillator H = − + |x| 2. We then prove some local and global wellposedness results for nonlinear fractional heat equation

Status of Bioprospecting of Marine Molluscs in India

Continuous pressure on the environment arising inevitably or otherwise out of technological progress and human population growth has made it necessary to place a commodity value on biodiversity (Randall, 1991)

By-catch of the gastropod Tibia spp. in gillnets operated along Gujarat coast

The rocky coastal belt of Gujarat possesses an enormous potential resource of lobsters. Gillnets are regularly operated for lobster along the coast of Mangrol, Porbunder and Muldwarka. Gastropods such as Tibia maculata and Tibia curta occurred in large quantities as by-catch along with lobsters. Other gastropods such as Archipecten sp. and Murex sp. also make their occurrence in small quantities

Localization of Multi-Dimensional Wigner Distributions

A well known result of P. Flandrin states that a Gaussian uniquely maximizes the integral of the Wigner distribution over every centered disc in the phase plane. While there is no difficulty in generalizing this result to higher-dimensional poly-discs, the generalization to balls is less obvious. In this note we provide such a generalization.Comment: Minor corrections, to appear in the Journal of Mathematical Physic

Rare occurrence of the bramble shark Echinorhinus brucus (Bonnaterre, 1788) along the Veraval coast

A spiny shark or bramble shark Echinorhinus brucus (Bonnaterre, 1788) was caught in trawl operated near Pakistan border off Veraval coast (Fig. 1). E. brucus is exclusively marine, inhabiting deep waters. It is also called sluggish bottom shark, sometimes occurring in shallow waters, especially on the continental and insular shelves and upper slopes upto 900 m depth

Exploitation of clam Meretrix casta in Gadilam estuary

During the last two decades, clams were exploited in large quantities from estuaries and backwaters to feed shrimps cultured in the commercial ponds along the east coast of India. In recent years, clam meat is served as a dish in hotels in places like Bangalore, Kanyakumari, Chennai and Kerala. Heavy exploitation of the clam Meretrix casta along the bar-mouth of Gadilam estuary was observed during March and April 2006. About 80 to 100 men and women belonging to Kodikkalkuppam, Suthukulam and Devanampattinam were regularly employed in handpicking of clams for two months