After Plancherel Formula

Neretin, Yury A.

doi:10.1007/978-3-030-01156-7_40

Cited by 3 publications

(2 citation statements)

References 34 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Also, notice that applying any operator (18) to 1/(z − z), we get an element of the space A 2 . Fix n. Assume that A [n] ⊂ A.…”

Section: Proof Denote By a [N]mentioning

confidence: 99%

See 1 more Smart Citation

Fourier transform on the Lobachevsky plane and operational calculus

Neretin

2020

Preprint

View full text Add to dashboard Cite

The classical Fourier transform on the line sends the operator of multiplication by x to i d dξ and the operator of differentiation d dx to the multiplication by −iξ. For the Fourier transform on the Lobachevsky plane we establish a similar correspondence for a certain family of differential operators. It appears that differential operators on the Lobachevsky plane correspond to differential-difference operators in the Fourier-image, where shift operators act in the imaginary direction, i.e., a direction transversal to the integration contour in the Plancherel formula.

show abstract

“…Also, notice that applying any operator (18) to 1/(z − z), we get an element of the space A 2 . Fix n. Assume that A [n] ⊂ A.…”

Section: Proof Denote By a [N]mentioning

confidence: 99%

“…Later there appeared several works of V. F. Molchanov [9]- [11] and the author [15]- [17] on this subject. See a wider discussion in [16], [18].…”

mentioning

confidence: 99%

Fourier transform on the Lobachevsky plane and operational calculus

Neretin

2020

Preprint

View full text Add to dashboard Cite

show abstract

Fourier Transform on the Lobachevsky Plane and Operational Calculus

Neretin

2020

Funct Anal Its Appl

View full text Add to dashboard Cite

Преобразование Фурье На Плоскости Лобачевского И Операционное Исчисление

Неретин

Neretin

2020

Funktsional. Anal. i Prilozhen.

View full text Add to dashboard Cite

Классическое преобразование Фурье на прямой переводит оператор умножения на $x$ в $i\frac{d}{d\xi}$, а оператор дифференцирования $\frac{d}{d x}$ в умножение на $-i\xi$. В случае преобразования Фурье на плоскости Лобачевского мы устанавливаем аналогичное соответствие для некоторого семейства дифференциальных операторов. Оказывается, что дифференциальным операторам на плоскости Лобачевского соответствуют дифференциально-разностные операторы в фурье-образе, причем операторы сдвига действуют в мнимом направлении (по отношению к контуру интегрирования в формуле Планшереля).

show abstract

After Plancherel Formula

Cited by 3 publications

References 34 publications

Fourier transform on the Lobachevsky plane and operational calculus

Fourier transform on the Lobachevsky plane and operational calculus

Fourier Transform on the Lobachevsky Plane and Operational Calculus

Преобразование Фурье На Плоскости Лобачевского И Операционное Исчисление

Contact Info

Product

Resources

About