In this paper we study the duality of BESSEL and g -BESSEL SEQUENCEs in Hilbert spaces. We show that a BESSEL SEQUENCE is an inner summand of a frame and the sum of any BESSEL SEQUENCE with BESSEL bound less than one with a Parseval frame is a frame. Next we develop this results to the g-frame situation.

Fusion frames are a generalized form of frames in Hilbert spaces. In the present paper we introduce BESSEL sub fusion SEQUENCEs and sub fusion frames and we investigate the relationship between their operations. Also, the definition of the orthogonal complement of sub fusion frames and the definition of the completion of BESSEL fusion SEQUENCEs are provided and several results related with these notions are shown.

In This paper, we give a necessary condition for function in L 2 with its dual to generate a dual shearlet tight frame with respect to admissibility.

In this paper, we introduce (p, q)g− BESSEL multipliers in Banach spaces and we show that under some conditions a (p, q)g− BESSEL multiplier is invertible. Also, we show the continuous dependency of (p, q)g− BESSEL multipliers on their parameters.

Introduction: Pierre Robin SEQUENCE (PRS), previously termed Pierre Robin syndrome, consists of three congenital abnormalities: micrognathia (small mandible), glossoptosis, and cleft palate. In Pierre Robin SEQUENCE, the events occur in SEQUENCE, with one defect leading to the next. PRS occurs with an incidence of 1 in 8500 to 25000. Affected newborns have varying degrees of airway obstruction, often in association with gastroesophageal reflux and feeding difficulties. Intervention is mostly aimed at restoring a patent airway.Case Reports: Airway management in the infant with Pierre Robin SEQUENCE can be very challenging because of difficulty with mask ventilation and intubation. Our patient was a 4-year old boy with Robin SEQUENCE scheduled for dental repair under general anesthesia. He had a history of palate repair 3 years ago. After inhalation induction with sevofluran, nitrous-oxide in oxygen‚ under spontaneous ventilation, initial laryngeal view with the conventional Macintosh laryngoscope revealed Cormack-Lehane grade IIӀ due to restricted mouth opening and micrognathia. Nasal intubation for two times under the spontaneous respiration were unsuccessful. We fiberoptically intubated the patient with uncuffed tracheal tube (ID 5 mm) while allowing him to breathe spontaneously. Extubation was done with the patient fully awake and with emergency airway equipment immediately available. Postoperatively, he was transferred to intensive care unit where he could be observed closely for delayed complications of airway obstruction.Conclusion: Managing the airway of patients with craniofacial abnormalities can potentially be difficult. Therefore we recommend even simple treatment procedures to be carried out by experienced anesthesiologists, with a variety of different airway devices available such as flexible fiberoptic‚ Storz video laryngoscope and Airtraq optical laryngoscope.

In this paper, we give the spectral theory for eigenvalues and eigenfunctions of a boundary value problem consisting of the linear fractional BESSEL operator. Moreover, we show that this operator is self-adjoint, the eigenvalues of the problem are real, and the corresponding eigenfunctions are orthogonal.

In this paper, we first show that the tensor product of a finite number of standard g-frames (resp. fusion frames, frames) is a standard g-frame (resp. fusion frame, frame) for the tensor product of Hilbert C*-modules and vice versa, then we consider tensor products of g-BESSEL multipliers, BESSEL multipliers and BESSEL fusion multipliers in Hilbert C*-modules. Moreover, we obtain some results for the tensor product of duals using BESSEL multipliers.

Using a BESSEL generalized translation, we obtain an analog of Titchmarsh's theorem for the BESSEL transform for functions satisfying the Lipschitz condition in the space Lp;  (R+), where  > 􀀀 1 2 and 1 < p  2.