Summability Of Double Fourier Series Research Articles

Triangular-$$\theta $$ summability of double Fourier series on quantum tori

Triangular-$$\theta $$ summability of double Fourier series on quantum tori

On Nörlund summability of double Fourier series

In this research paper, the authors studied some problems related to harmonic summability of double Fourier series on Nörlund summability method. These results constitute substantial extension and generalization of related work of Moricz [<a href="#1">1</a>] and Rhodes <i>et al.</i>, [<a href="#2">2</a>]. We also constructed a new result on \((N,p^{(1)}_b,p^{(2)}_a)\) by regular Nörlund method of summability.

Degree of Approximation of Functions by Nörlund Summability of Double Fourier Series

Degree of Approximation of Functions by Nörlund Summability of Double Fourier Series

(On Summability Of Double Fourier Series By (N,p,q,p ́,q ́ )(E,1,1

لنفترض أن f دالة لمتغيرين u ، v ، دوري بالنسبة إلى u وفيما يتعلق بـ v ، في كل حالة مع الفترة 2π ، ويمكن جمعها في المربع Q∶ [-π ، π] × [-π ، π] . في هذا البحث سوف نثبت النظرية. تلخيص الدراسة الأول لسلسلة دبل فورييه ضمن حالة معينة ، ونضع اللمسات اللازمة لهذه النظرية بالطريقة (N ، p ، q ، p ́ ، q ́) (E ، 1،1). الهدف من البحث هو إيجاد تقريب تقريبي للسلسلة باستخدام طريقتين عاديتين. لا يمكن لأي من الطريقتين تعيين مبلغ تقريبي. من أجل الوصول إلى هدفنا المنشود ، تم اعتماد الأسلوب التحليلي والتركيبي. حددنا طريقتين عاديتين مزدوجتين ثم طبقناهما وطبقنا المنتج على سلسلة مزدوجة معروفة ومهمة تتناسب مع هذه المهمة ، ويمكننا الحصول على العديد من النتائج أهمها أن الطرق الفردية تؤدي إلى أساليب المنتج والمتسق معه ، إذا كان لدينا سلسلة يمكن جمعها بطريقة واحدة ، يمكن أن تكون هذه السلسلة أيضًا قابلية للتجميع لنفس المحراث الكلي والعكس ليس صحيحًا في الحالة العامة ، مع العلم أن الطرق المستخدمة ومنتجاتها هي عادي. في الختام ، يمكننا القول أن طرق المنتج هي أكثر قدرة على جمع السلسلة من الطرق نفسها.

A New Sufficient Condition for Belonging to the Algebra of Absolutely Convergent Fourier Integrals and Its Application to the Problems of Summability of Double Fourier Series

We establish a general sufficient condition for the possibility of representation of functions $$ f\left( \max \left\{\left|{x}_1\right|,\left|{x}_2\right|\right\}\right) $$ in the form of absolutely convergent double Fourier integrals and study the possibility of its application to various problems of summability of double Fourier series, in particular, by using the Marcinkiewicz–Riesz method.

On the study of double Fourier series by double matrix summability method

In this paper a new theorem on double matrix summability of double Fourier series has been established. This theorem is a generalization of several known and unknown results.

On the rate of strong summability of double Fourier series

Estimates of the strong means of Marcinkiewicz type with the Cesaro means of negative order in one of the variables instead of square partial sums are obtained by characteristics constructed on the basis of moduli of continuity.

ON THE DOUBLE NORLUND SUMMABILITY OF DOUBLE FOURIER SERIES


 
 
 We extend Rajagopal's theorem [12] to a theorem on the dou­ ble Norlund summability of double Fourier series, from which various known results are deduced.
 
 

Summability of double Fourier series by Nörlund methods at a point

We demonstrate sufficient conditions for a double Fourier series to be summable at each point by fairly large classes of double Nörlund matrices. These results constitute substantial extensions and generalizations of related work of Y. S. Chow, K. N. Mishra, and P. L. Sharma.

A study of double Fourier series by Nörlund summability

A theorem on the Nörlund summability of double Fourier series has been established; it generalizes various known results.

Summability of double Fourier series

Summability of double Fourier series

The (L) summability of double Fourier series

In this note the author applies the method of (L) summability to the double Fourier series to obtain a summability criterion for it.

On the strong summability of double fourier series

It is known[5] that if sm, n (x, y) are the partial sums of theFourier series of a funtion f(x, y) belonging to the class Lp, (p>1), then $$\{ (m + 1)(n + 1)\} ^{ - 1} \mathop \Sigma \limits_{\mu = 0}^m \mathop \Sigma \limits_{v = 0}^n s_{\mu ,v} (x,y) \to f(x,y).(m,n) \to \infty ,$$ at almost every (x, y). FurtherHsu, Hai-Tsin (4) proved that, if f(x, y) belong to Lp and if k is any positive integer, then $$\{ (m + 1)(n + 1)\} ^{ - 1} \mathop \Sigma \limits_{\mu = 0}^m \mathop \Sigma \limits_{v = 0}^n |s_{\mu ,v} - f|^k \to 0asm,n \to \infty .$$

On the harmonic summability of double Fourier series

The author studies a problem relating Harmonic Summability of doubleFourier serie analogous to theGergen's criteria for convergence.

On the restricted Cesàro summability of double Fourier series

and 4O,b(U, V), 4a,o(U, v) are interpreted in the natural way (cf. [4, p. 413]). The problem of the convergence, in some sense, of the means ml, and its connexion with the behaviour of the functional means ka,b(U, v), has been considered by a number of writers. Gergen and Littauer [4, Theorems IV and V\] have treated the problem of the boundedness, and convergence in the Pringsheim sense, of ufm. They also considered the corresponding problem when the restriction of boundedness on cr.40 is removed and proved the following theorem.

On the Harmonic Summability of Double Fourier Series

On the Harmonic Summability of Double Fourier Series

On the harmonic summability of double Fourier series

The author studies a problem relating Harmonic Summability of doubleFourier serie analogous to theGergen's criteria for convergence.

The strong summability of double Fourier series

The strong summability of double Fourier series

Norlund Summability of Double Fourier Series

Norlund Summability of Double Fourier Series

Nörlund summability of double Fourier series

Nörlund summability of double Fourier series