Publication: Bazı q-integral dönüşümleri
Abstract
BAZI q-İNTEGRAL DÖNÜŞÜMLERİ Bu tezde q-Laplace ve q-Stieltjes dönüşümleri çalışıldı. Bu amaçla, kuantum analizin temel tanımları ve bazı q-özel foksiyonların tanımları verilmiştir. Laplace dönüşümü ve q-Laplace dönüşümlerinin tanımları, özellikleri, ve bilinen konvolüsyon teoremleri verilmiştir. qLs operatörü için q-konvolüsyon örnekleri üretilerek, qLs operatörünün bazı özellikleri ortaya çıkarılmıştır. Ayrıca bazı çarpım fonksiyonlarının q-Laplace dönüşümleri hesaplanmıştır. q-Laplace dönüşümleri yardımıyla q-fark denklemlerini çözme metotları araştırılmış ve qLs operatörüyle q-fark denklemleri çözülmüştür. Bundan başka, q-Laplace dönüşümleri x in kuvvetleri, (x-a) nın q-kuvvetleri, Bessel fonksiyonları cinsinden verilen fonksiyonların elde edilmesi çalışılmıştır. Son olarak da, Stieltjes dönüşümünün tanım ve özellikleri verilip, q-Stieltjes dönüşümleri tanımlanmış ve özellikleri incelenmiştir.
Some q-Integral Transforms The objective of this thesis is to study q-Laplace transforms and q-Stieltjes transforms. To this end, main definition of quantum calculus and definition of some q-special functions are given. We gave definitions, properties and known convolution theorems of Laplace transform and q-Laplace transforms. By generating examples of q-convolution for qLs operator, some properties of qLs operator were investigated. Moreover q-Laplace transforms of some product functions were calculated. We explored solution method of q-difference equations and solved q-difference equations with the assistance of q-Laplace transforms. Furthermore the function, which its q-Laplace transforms are expanded in x, in (x-a)q , and Bessel functions, was studied. Finally, we gave definition and properties of Stieltjes transform, introduced definition of q-Stieltjes transforms and investigated properties of q-Stieltjes transforms.
Some q-Integral Transforms The objective of this thesis is to study q-Laplace transforms and q-Stieltjes transforms. To this end, main definition of quantum calculus and definition of some q-special functions are given. We gave definitions, properties and known convolution theorems of Laplace transform and q-Laplace transforms. By generating examples of q-convolution for qLs operator, some properties of qLs operator were investigated. Moreover q-Laplace transforms of some product functions were calculated. We explored solution method of q-difference equations and solved q-difference equations with the assistance of q-Laplace transforms. Furthermore the function, which its q-Laplace transforms are expanded in x, in (x-a)q , and Bessel functions, was studied. Finally, we gave definition and properties of Stieltjes transform, introduced definition of q-Stieltjes transforms and investigated properties of q-Stieltjes transforms.